Entropies and the Anthropocene crisis

Maël Montévil

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 ∗
Entropies and the Anthropocene crisis
Maël Montévil†

July 29, 2020

Abstract
The contemporary Anthropocene crisis is frequently described as the rarefaction
of resources or resources per capita. However, both energy and minerals correspond
to fundamentally conserved quantities from a physical perspective. A specific con-
cept is required to understand the rarefaction of these resources. This concept,
entropy, pertains to the configurations of energy and matter and not just to their
sheer amount.
However, the physical concept of entropy is insufficient to understand biological
and social organizations. Biological phenomena display both historicity and more
synchronic, systemic properties. The concept of anti-entropy stems from the com-
bination of these aspects. We propose that many vulnerabilities of living entities
to the changes of the Anthropocene pertain to anti-entropy. They correspond to
the entropization of anti-entropy, that is, a loss of organization. They can also be
the disruption of anti-entropy production, that is to say, the loss of the ability to
produce functional novelties.

Keywords: entropy, anti-entropy, resources, organization, disruption, Anthro-

pocene

Contents
1 Introduction 2

2 Entropy in physics and application to available resources 3

2.1 Energy and entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Thermodynamic entropy . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Microscopic interpretations of entropy . . . . . . . . . . . . . . . 6
2.2 Dispersion and concentration of matter . . . . . . . . . . . . . . . . . . 11
2.2.1 Ore deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Wear and entropy . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Bioaccumulation, bioconcentration, biomagnification . . . . . . . 12
2.2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
∗
M. Montévil, Entropies and the Anthropocene crisis, AI and Society, Submitted.
†
Institut de Recherche et d’Innovation, Centre Pompidou

1
3 Entropy and organizations 14
3.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.1 Couplings with the surroundings . . . . . . . . . . . . . . . . . . 15
3.1.2 Micro spaces in biology . . . . . . . . . . . . . . . . . . . . . . . 16
3.1.3 Persisting organizations . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Disruptions as entropizations of anti-entropy . . . . . . . . . . . . . . . 19
3.3 The disruption of anti-entropy production . . . . . . . . . . . . . . . . . 21

4 Conclusion 23

1 Introduction
Despite cases of denial, citizens and governments increasingly acknowledge the Anthro-
pocene crisis. Nevertheless, this crisis requires further theoretical characterization. For
example, in the second “warning to humanity”, signed by more than 15000 scientists,
the arguments are convincing but are limited to the rationality of physics. The authors
exhibit quantities that are growing or shrinking exponentially (Ripple et al., 2017) and
it stands to reason that such a trend cannot persist in a finite planet. This line of
reasoning is commonplace in physics and shows that a change of dynamics is the only
possibility. For example, the said quantities may reach a maximum or the whole system
may collapse. However, is this line of reasoning sufficient to understand the Anthro-
pocene crisis and respond adequately to it?
Several authors have specified the diagnosis of the Anthropocene crisis. They argue
that this crisis is not a result of the Anthropos sui generis, but the result of specific
modes of organization of current human societies. Let us mention the concept of cap-
italocene (Moore, 2016). In the concept of capitalocene, the dynamics of capital is
the decisive organizational factor. The capital opened the possibility of indefinite ac-
cumulation abstracted from other material objects. Along a similar line, the concept
of plantationocene posits that the plantation is the damaging paradigm of social orga-
nizations and relationships to other living beings (Haraway, 2015; Davis et al., 2019).
In both cases, the focus is on human activities and the reason why they are destruc-
tive for their conditions of possibility. These accounts provide relevant insights but are
insufficient in their articulation with natural sciences.
To rearticulate economics and natural processes, Georgescu-Roegen (1993) empha-
sized the theoretical role of entropy. Economists should part with the epistemology
of classical mechanics where conservation principles and determinism dominate. In
thermodynamics, the degradation of energy is a key concept, that is, the irreversible
increase of entropy. Methodologically, the implication is that economists should take
into account the relevant knowledge about natural phenomena instead of working on
self-contained mathematical models.
This work has been reinterpreted by Stiegler (2018). B. Stiegler argues that the
hallmark of the Anthropocene is the growth of relevant entropies at several levels of
analysis, including at the level of social activities. In this paper, we will discuss sev-
eral aspects of this idea with a focus on mathematized situations or situations where
mathematization is within sight.
We first explain why entropy is a critical concept to understand the “consumption” of
energy resources. We provide a conceptual introduction to the thermodynamic concept
of entropy that frames these processes in physics. Similarly, we will discuss resources
such as metals and argue that the property impacted by biological and human activity

2
is not their amount on Earth but their configuration. Concentrations of metals increase
when geological processes generate ore deposits. On the opposite, the use of artifacts
can disperse their constituents. Last, compounds dispersed in the environment can be
concentrated again by biological activities, leading to the contamination of marine life
with heavy metals, for example.
To address biological organizations and their disruptions, we first develop several
theoretical concepts. The epistemological framework of theoretical biology differs rad-
ically from equilibrium thermodynamics. We introduce the concepts of anti-entropy
and anti-entropy production that mark a specific departure from thermodynamic equi-
librium. We show that they enable us to understand critical destructive processes for
biological and human organizations.

2 Entropy in physics and application to available resources

In this section, we will discuss two kinds of resources relevant to the economy and show
that the proper understanding of these resources requires the concept of entropy in the
physical sense of the word. The first case that we will discuss is energy, and the second
is elements such as metals.

2.1 Energy and entropy

The stock of energy resources is commonly discussed in economics and the public debate.
However, it is a fundamental principle of physics that energy is conserved. It is a
physical impossibility to consume energy stricto sensu. For example, a falling ball is
transferring potential energy into kinetic energy, and if it bounces without friction,
it will reach the initial height again, transforming kinetic energy back into potential
energy. This remark is made repeatedly by physicists and philosophers but does not
genuinely influence public discourses (Mosseri and Catherine, 2013). Georgescu-Roegen
(1993) and authors who built on his work are an exception.
To dramatize the importance of this theoretical difficulty, let us mention that the
increase in the temperature of a body implies the increase of its internal energy. Heat
engines, including thermic powerplants, are a practical example of this: they transform
heat into useful work (useful motion). We are then compelled to ask an unexpected
question. Why would climate change and the subsequent increases in temperature not
solve energy crises?

2.1.1 Thermodynamic entropy

The greenhouse effect keeps the energy coming from the sun on Earth, and at the same
time, the shrink of resources such as oil leads to a possible energy crisis. The main
answer to this paradox is that not all forms of energy are equivalent.
Let us picture ourselves in an environment at a uniform temperature. In this situa-
tion, there is abundant thermic energy environing us, but there is no means to generate
macroscopic motions from this energy. We need bodies at different temperatures to
produce macroscopic motions. For example, warming up a gas leads to its expansion
and can push a piston. If the gas is already warm, it cannot exert a force on the said
piston. It is the warming up of the gas that generates useful work, and this process
requires objects with different temperatures.
An engine requires a warm and a cold source to sustain a temperature difference.
This rationale led to design cycles where, for example, a substance is warmed up and

3
cooled down iteratively. These cycles are the basis of heat engines. XIXth century
physicists, in particular, Carnot and Clausius, theorized these cycles. When generating
macroscopic motion out of thermic energy, the maximum efficiency of the engine is
limited.1 The efficiency depends on the ratio of temperatures of the cold and the warm
sources. When the temperatures tend to become equal, the efficiency decreases and
tends to zero. Physicists introduced entropy to theorize heat engines’ efficiency. As a
side note, nuclear powerplants use the same principle, where the warm source is atomic
fission, and the cold source is a river or the sea.
Now, let us consider that we have warm water and cold water and that we pour
them together in a pot. After some time, the water will reach a uniform temperature,
and we have lost the chance to extract mechanical work out of the initial temperature
difference. This phenomenon is remarkable because it displays a temporal direction: we
have lost the ability to do something. Theoretically, this kind of phenomena defines a
time arrow that classical mechanics lacks.2 Likewise, it is possible to generate heat out
of mechanical work by friction, including in the case of electric heaters, but, as we have
seen, the opposite requires two heat sources at different temperature.
Energy is a conservative quantity following the first principle of thermodynamics.
The only way to remove energy from a system is to put it outside of the system. Being
conservative should not be confused with being conserved. The energy of a system is
not necessarily conserved; it can decrease if it is released outside, or increase if some
energy comes from outside.
In this context, what is entropy? The classical thermodynamic perspective defines
entropy as a quantity describing the state of a system together with other quantities
like energy, volume, . . . Physicists used to think of heat as the exchange of an abstract
fluid, the “caloric”; however, the possibility of a complete transformation of work into
heat and the partial conversion of heat into work is not amenable to the definition of
such a fluid. Nevertheless, the notion of fluid remains partially relevant to understand
what entropy abstractly is. Entropy is proportional to the size of a system, like the
mass or energy. Entropy can be exchanged, and in special situations called reversible,
entropy is conservative, like energy.
However, the difference between entropy and energy is that entropy tends to increase
towards a maximum in an isolated system, following the second principle of thermody-
namics. This statement has two implications: i) entropy is not conservative in general
and ii) the non-conservative changes of entropy are only increases. In reversible sit-
uations, entropy is conservative. By contrast, irreversibility leads to the concept of
entropy production: a net increase of entropy that does not stem from flows with the
surroundings.
Here again, being conservative is not the same than being conserved, and entropy
production is the departure from entropy being conservative. Nicolis and Prigogine
(1977) showed that a system can produce entropy continuously and still be stationary
if the entropy produced flows to the surroundings. Here, the entropy of the system is
conserved, but it is not conservative. Similarly, the entropy of a system can decrease
when work is used to this end. For example, centrifugation separates compounds of a
gas or a liquid.
The second principle of thermodynamic captures the idea that heat can only go
from warm bodies to cold bodies. The entropy change due to a heat exchange Q is
dS = Q/T , where S is the entropy, and T is the temperature. Then, if we have
1
This efficiency is defined as the work produced divided by the heat taken from the warm source.
2
The concept of a time arrow is somewhat abstract. Intuitively, there is a time arrow if we can tell
whether a movie is played forward or backward by fundamental principles (Gayon and Montévil, 2017).

4
a isolated system with two bodies at temperature Th > Tc , exchanging heat, then
dS = Qc→h /Th + Qh→c /Tc . We assume that the objects are only exchanging heat
between each other so that Qc→h = −Qh→c . The only way for dS to be positive is if
Qh→c is positive; that is, the energy is going from the warm body to the cold body.
In classical thermodynamics, the central concept is thermodynamic equilibrium. At
equilibrium, there are no macroscopic net fluxes within the system and with the system
surroundings. For example, if we consider an open room, thermodynamic equilibrium
is met when temperature, pressure, and other variables are homogeneous and the same
as the surroundings. There are always exchanges of gas with the surroundings, but
on average, there are no fluxes. By contrast, Nicolis and Prigogine (1977) describe
stationary configuration far from thermodynamic equilibrium because there is a net
flow of entropy from the system to the surroundings.
Thermodynamic equilibrium is typically the optimum of a function that is the com-
bination of state variables appropriate for a given coupling with its surroundings. For
example, entropy is maximal for an isolated system at thermodynamic equilibrium.
Helmholtz free energy F describes the useful work that can be obtained from a system
at constant temperature and volume. Let us discuss F = U − T S where U is the in-
ternal energy. T S corresponds typically to the energy in the thermic form so that F is
the energy minus the internal energy in thermic form. Spontaneously, Helmholtz free
energy will tend to a minimum. This property is used in engineering to design processes
leading to the desired outcome.
Helmholtz free energy is not the most commonly used function. Consider a battery in
ordinary conditions; its purpose is to provide electrical work to a circuit, a smartphone
say. Part of the work that can be performed by the battery is its dilation, which will
push air around it. However, this is not genuinely useful. This kind of situation leads to
the definition of Gibbs energy, the maximum amount of non-expansion work that can
be obtained when temperature and pressure are set by the surroundings, G = F + pV ,
where p is pressure and V is volume.
In these examples, couplings with surroundings are a manifestation of technological
purposes. Sometimes, the concept of exergy is used to describe available energy in
general. Unlike Helmholtz and Gibbs free energy, exergy is not a function describing
the state of a system because it depends on the coupling with the system surroundings.
it depends on circumstances and can be aggregated in general.
Classical mechanics is deterministic and provides the complete trajectories of the
objects described. By contrast, thermodynamics only determines the final state of a
system by the minimization of the appropriate function. Since this state is singularized
mathematically as an extremum, theoreticians can predict it. The epistemological effi-
cacy of this theory lies precisely in the ability to determine final states. A system can
go from the initial situation to the final situation by many paths, but the outcome is
the same. Calculations are performed on well defined, theoretical paths, whereas actual
path may involve situations such as explosions where variables like entropy are not well
defined (they are defined again at equilibrium).
Classical thermodynamics is about final states at thermodynamic equilibrium. There
is no general theory for far from thermodynamic equilibrium situations. The study of
these situations may or may not use thermodynamic concepts. For example, biological
evolution or linguistic phenomena all happen far from thermodynamic equilibrium, but
their concepts are not thermodynamic. By contrast, non-equilibrium thermodynamics
such as the work of Nicolis and Prigogine (1977) use concepts of thermodynamics. Unlike
classical thermodynamics, these approaches need to introduce an accurate description
of the dynamics. A standard method is to assume that small parts of the system are at

5
or close to thermodynamic equilibrium, but that globally the system is far from it.
To sum this discussion up, entropy is abstractly similar to a fluid to an extent. The
limit of this analogy is that entropy is not conservative and spontaneously tends to a
maximum in an isolated system. We do not genuinely consume energy; we are producing
entropy. However, this does not lead to a straightforward accounting of entropy produc-
tion on Earth. Earth is far from equilibrium, and its entropy is not well defined. Locally,
exergy (usable energy) is not a state function since it depends on the couplings between
a system and its surroundings. It follows that we cannot aggregate exergy between
systems with a different nature. Nevertheless, in the comparison of physically similar,
local processes, entropy production and exergy are relevant and necessary concepts.
In this context, it is interesting to note that an increase in temperature leads to an
increase in entropy. As such, if Earth’s entropy were defined, global warming would
increase it. At the same time, Earth is exposed to the cold of space vacuum and loses
heat this way. The greenhouse effect slows down this process, and thus slows down the
corresponding production of entropy (released in open space). Accordingly, if we had a
machine that was using the heat of the Earth surface as a warm source and the open
space as a cold source, global warming would lead to more usable energy. Of course,
this principled analysis has no practical counterpart. With this last example, we aim
to emphasize again that the assessment of entropy and entropy production should be
performed with respect to technological or biological processes.

2.1.2 Microscopic interpretations of entropy

The thermodynamic perspective described above is somewhat abstract; however, it has
two microscopic interpretations which were introduced by Boltzmann and Gibbs, respec-
tively. Debates on which of this interpretation is more fundamental are still ongoing,
and their prevalence also has geographical differences (Goldstein et al., 2019; Buonsante
et al., 2016). For large isolated systems, they lead to identical conclusions despite their
conceptual differences. Both are bridges between microscopic and macroscopic descrip-
tions. Here, we assume that the microscopic description is a classical, deterministic
dynamics, and we do not address the quantum case.
Let us start with Boltzmann’s interpretation of entropy. We consider gas in an
insulated container so that its energy is constant. At the microscopic level, molecules
move and bump on each other and the walls of the container chaotically. At this level,
particles are described by their positions and velocities in three dimensions. These
numerous quantities define together the microstate, X, and the micro space, i.e., the
mathematical space of possible microstates. Let us insist that the microstate is not
small; it describes all particles, thus the whole system. Then, we define the possible
macrostates. For example, we posit that one macrostate corresponds to a uniform
concentration of the molecules at a given scale and with a given precision. We can
define another macrostate where all the particles are in the corner of the box, and one
that encompasses all other possibilities. Depending on the microstate X, we will be in
one of the three possible macrostates.
Let us follow Boltzmann and call Ω(X) the volume of the micro space that corre-
sponds to the same macrostate than X. There are two crucial points in Boltzmann’s
reasoning on Ω.
First, the microscopic volume of a particular macrostate is overwhelmingly higher
than the one of others. This situation is a mathematical property that stems from the
huge number of particles involved. As a mathematical illustration, let us throw coins.
Heads are 1, and tails are 0. The macroscopic variable is the average of the result after

6
a series of throws, which can go from 0 to 1. The first macrostate (M1 ) is met when this
average is between 0.48 and 0.52. All other possibilities lead to the other macrostate
(M2 ). With four throws we get, for example 0011 → 0.5 (M1 ), 0110 → 0.5 (M1 ),
0010 → 0.25 (M2 ), 1110 → 0.75 (M2 ), 1110 → 0.75 (M2 ) and so on. The macroscopic
results are quite random. However, for 10000 throws, with simulations, we get 0.493
(M1 ), 0.499 (M1 ), 0.505 (M1 ), 0.512 (M1 ), 0.498 (M1 ) and so on. The system is always
in the first macrostate even though it covers a small part of the possible macroscopic
values.
Second, Boltzmann assumes molecular chaos: the system explores the micro space
uniformly. It follows that the time spent by the system in a given macrostate is pro-
portional to the microscopic volume of this macrostate.
Since one macroscopic possibility corresponds to an overwhelming part of the micro
space, the system will spontaneously go in this domain and remain there except for
possible, rare and short-lived periods called fluctuations. The largest the number of
particles, the rarest fluctuations are. In typical situations, the number of particles is
not 4 or 10000, but is closer to 1000000000000000000000; therefore, fluctuations do not
matter.
Ω(X) tends to a maximum with vanishingly rare fluctuations. It is a way to interpret
the second principle of thermodynamics, which states that entropy cannot decrease in
an isolated system. For example, why all air molecules are not in one corner of the
room? Because all microscopic situations are equally likely and there are far more
microscopic configurations that correspond to a uniform concentration of air than any
other macrostate, see figure 1.
As pointed out by Chibbaro et al. (2014), this notion is very intuitive. For example,
when playing pool, the initial situation is improbable, and we spontaneously think that
somebody had to order the pool balls for them to be in a triangle shape. After striking
them, their configuration becomes more uniform, and we acknowledge that it is the
result of multiple random collision. The same qualitative result will follow if we throw
balls randomly on the table. It is the same for velocities. Initially, only the ball struck
is moving, and all others are still. After the collision, the kinetic energy is distributed
among the balls until friction stops them. Of course, the goal of the game is to go
beyond randomness and players aim for balls to reach specific locations.
The number of possibilities Ω is a multiplicative quantity. For example, if we throw
a coin, there are 2 possibilities, but if we throw three coins, there are 2 × 2 × 2 = 8
possibilities. This mathematical situation does not fit with the idea that entropy is
proportional to the size of a system, which is part of the classical definition. The
logarithm function transforms multiplication into addition, so log(Ω1 × Ω2 ) = log(Ω1 ) +
log(Ω2 ). Then log(Ω) fits the properties of entropy, and we can state with Boltzmann
that:

S = kB log(Ω(X)), where kB is a constant

Of course, there are many refinements of this approach to entropy. Here, for example,
we considered that the total energy is conserved, whereas it is not always the case. Then,
the definition of macrostates must include energy.
Gibbs proposed a different conceptual framework to interpret thermodynamic en-
tropy (Goldstein et al., 2019; Sethna, 2006). Instead of studying a single system, Gibbs
study an ensemble of systems, where we describe microstates by their probabilities.
In particular, the fundamental postulate of statistical mechanics states that all mi-
crostates with the same energy have equal probability in an isolated system. This

7
 Macrostates
ABC D E

Ω(X)

Figure 1: Illustration of Boltzmann entropy. Here, the micro space is represented

schematically in 2 dimensions, and colors represent the corresponding macrostates. The
system starts from a microstate associated with macrostate A. It explores microstates
uniformly and soon arrives in positions corresponding to the macrostate E because most
microstates correspond to E. For a microstate X, the number of configuration leading
to the macrostate is Ω(X) (in light blue). Note than in physical cases, the micro space
is not in 2 dimensions but has a huge number of dimensions — it is often the space of
positions and momenta of all molecules, which leads to 3 + 3 = 6 quantity per particle.

ensemble is called the microcanonical ensemble — this is Boltzmann’s hypothesis in a

different conceptual context.
Then, except for temperature and entropy, the macroscopic quantities are averages
of the microscopic quantities computed with the probabilities defining the ensemble.
The Gibbs entropy is defined by:
X
S = −kB ρi log(ρi ), where ρi is the probability of the microstate i
i

Despite their formal similarity, Gibbs and Boltzmann’s formulations have a critical
difference. In Boltzmann’s formulation, a single microstate has an entropy: a microstate
corresponds to a macrostate, this macrostate corresponds to many microstates, and how
many define the entropy of the said microstate. By contrast, Gibbs framework is not
about individual microstates, and we consider all possible microstates simultaneously.
Some are more probable than others, and entropy is about the probabilities assigned to
the microstates. For example, when the system is isolated, and its total energy is con-
stant, all microstates with the same energy have equal probability, and this maximizes
the entropy.
In a nutshell, the entropy being maximal is a property of the state of the system for
Boltzmann. By contrast, it is a property of an ensemble of systems for Gibbs, and more
specifically, it is a property of the associated probabilities. In mathematically favorable
conditions (infinite number of particles), the outcome is the same despite this significant

8
Figure 2: Coarse-graining versus Liouville’s theorem. As in figure 1, space is repre-
sented schematically in 2 dimensions. The micro space is coarse-grained by a grid. The
systems are initially in a small part of the micro space, which corresponds to four boxes
of the coarse-grained grid. After some time, the initial volume has deformed without
expanding at the fine-grained level in green. However, the coarse-grained volume occu-
pied by the systems has expanded in blue. After more time, the fine-grained volume
has become highly convoluted and meets the whole coarse-grained space, in blue. The
growth of the coarse-grained volume occupied by the systems is the argument explaining
the growth of Gibbs entropy.

conceptual difference.
Gibbs formulation presents a hidden challenge. Liouville’s theorem’s states that the
probabilities in an initial volume in the micro space are conserved over the dynamics.
It follows that this volume cannot shrink or expand over time. Taken as is, this would
mean that the entropy cannot increase over time — an embarrassing result when aiming
to interpret the second principle of thermodynamics.
The leading solution to this problem is a procedure called coarse-graining. Let us
introduce it by an analogy. Water occupies a small volume in the tank of a spray
bottle. Once water is sprayed, a tissue in the air affected is going to be wet. From the
perspective of the tissue, water occupies a vast volume of air. Nevertheless, the actual
volume of liquid water remains the same; water has just been dispersed, not added.
This example shows that there are two ways to understand the volume of water: the
fine-grained volume of water that remains the same, and the volume of air where the
moving tissue will meet water this volume increases. Mathematically, if we partition
space in boxes, all these boxes will contain some of the sprayed water. This procedure
is called a coarse-graining. The fine-grained volume of water remains the same, but the
coarse-grained volume has expanded (figure 2).
Technically, the microstates are not represented individually in the calculation of
entropy because entropy would not change over time as a result of Liouville’s theorem.
Instead, physicists use a coarse-grained representation of the system, where probabilities
describe each volume. The dynamics still preserve the fine-grained volume; however,
the latter deforms, gets more and more convoluted over time, and meets more and more
coarse-grained volumes (the boxes). As a result, the coarse-grained volume increases,
and so does the entropy (figure 2).
Let us make several supplementary remarks.
First, the second principle of thermodynamic is imperative: the entropy of an isolated
system cannot decrease. In Boltzmann’s formulation, entropy can also decrease albeit
overwhelmingly rarely. In Gibbs formulation, the equilibrium probabilities remain as
such, so entropy can only increase.

9
 Second, the concept of entropy in physics pertains to physics. The hallmark of this
theoretical nature is the use of the constant kB . kB is the bridge between tempera-
ture, heat and mathematical entropy since an exchange of heat leads to Q/T = dS =
kb d log Ω. kB bridges units of the International System of Units. Sometimes, a similar
mathematical apparatus can be used, for example, to study flocks of bird or school of
fishes (Mora and Bialek, 2011); however, this use is an analogy and does not convey
the same theoretical meaning (Montévil, 2019c). The absence of kB is evidence of this
fact. Along the same line, in physics, the space of possible microscopic configurations
inherited from mechanics is position and momenta, and other aspects can be added,
such as molecular vibrations or chemical states.
Third, why does an isolated system tends towards maximum entropy, in a nutshell?
Let us imagine that the system starts in a low entropy configuration. In Boltzmann’s
formulation, it will travel among microstates, and most microstates correspond to a
single macrostate, which is the maximum entropy configuration (the microstate of a
system explores the micro space uniformly). In Gibbs formulation, let us picture that
initially, the ensemble of systems is confined to a single coarse-grained microstate. Over
time, it will spread towards more and more coarse-grained microstates so that their
probabilities will tend towards the equilibrium distribution, the one with maximum
entropy.
In both cases, the macroscopic description of the object goes from a particular
state towards the most generic configuration, and the increase of entropy erases the
macroscopic peculiarity of the initial configuration. It erases the past. The increase of
entropy corresponds to the spread among microstates towards more generic microstates.
As such, we can interpret it as the dispersion of energy. Nevertheless, the increase of
entropy is sometimes compatible with the appearance of macroscopic patterns. They
can emerge due to energetic constraints, in the formation of crystals such as ice for
example. However, to enforce further patterns, work is required. For example, the
Earth’s gravity field pulls heavier molecules to the bottom of a room, which has many
implications for toxic gases.
Last, the articulation of the objective and subjective dimensions of entropy is a
complex subject. Let us mention an interesting example given by Francis Bailly: when
scientists discovered isotopes, seemingly equivalent particles could be distinguished.
The macroscopic description changed, and so did the entropy. The decisive point is
that previous predictions still hold. For example, if gas is initially in the corner of a
room, it will spread in the room. However, we can make new predictions once we know
that there are different isotopes. For example, if we see that only a given isotope is in
the corner of the room, then we can predict that the corresponding entropy will increase
and that the molecules with this isotope will spread in the room.
Along the same line, Boltzmann’s formulation depends on the definition of macrostates.
The latter depends on the coupling between the system and its surroundings. Similarly,
Gibbs entropy depends on a coarse-graining, which also corresponds to the coupling
between a system and its surroundings. Thus, entropy ultimately depends on these
couplings. As a result, Rovelli (2017) argues that entropy and the corresponding time
arrow are perspectival, where the perspectives are not merely subjective but stem from
the couplings with surroundings. In the case of technlogies, the choice of the couplings
depend on the purpose of the device, as discussed above.

10
2.2 Dispersion and concentration of matter
In this section, we will discuss how entropy underlies the theoretical understanding of
mineral resources. This case is relatively simple since we are mostly concerned with the
phenomena of dispersion and concentration of matter.
Georgescu-Roegen (1993) struggled with this question and even considered a possible
fourth law of thermodynamics to state that perfect recycling is not possible. The current
consensus is that this point is not valid (Ayres, 1999; Young, 1991).
For example, Ayres (1999) argues that a “spaceship” economy is possible in principle.
In this mind experiment, free energy comes from outside ad libitum, and the matter is
recycled thanks to this energy indefinitely. We mostly agree with this perspective except
on a specific point. If the system has to materialize its own boundaries (the shell of the
spaceship, or the atmosphere of the Earth), then these boundaries will be exposed to
the void of space and will be eroded — a phenomenon producing entropy. For example,
the Earth loses parts of its atmosphere continuously. However, this is more a principled
issue than a practical one, and it does not depend significantly on human activities.
At a more fundamental level, there is no sharp distinction between energy and
matter, as explained by Einstein’s equation E = mc2 . For example, the very slow decay
of protons is the destruction of what we usually consider as stable matter: it is a process
of entropy production.

2.2.1 Ore deposits

Despite these controversies, entropy is a critical concept to understand mineral re-
sources. In this section, we build mainly on the analysis of ore deposits formation in
geochemistry (Heinrich and Candela, 2014).
Non-radioactive atoms are conserved in chemical changes; therefore, human or bi-
ological activities do not alter their abundance on Earth.3 The problem of resources,
here, is similar to the one of energy: what matters is not the quantity of the intended
atoms existing on Earth. It is mostly their configurations.
When analyzing ore deposits, the critical factor is the concentration of the intended
ores. The higher the concentration of an ore deposit is, the less chemical and mechanical
work is required to purify it to useful levels, and, accordingly, the higher its profitability
is. If the local concentration of ores in the Earth crust was equal to its average every-
where, then even the most common resources could not be extracted fruitfully. Then,
it is the departure from situations of maximum entropy, as far as the concentrations of
ore are concerned, that is the crucial factor in analyzing mineral resources.
What is the origin of the heterogeneities that leads to usable ore deposits? If we
consider lava of the average composition of the Earth, in an insulated box, such deposits
would not appear spontaneously because of the second principle of thermodynamics.
However, the Earth is not in thermodynamic equilibrium. The nuclear fission of some
of its components warms its insides up — a transitory but prolonged process. Moreover,
it is an open system. The Sun provides energy on its surface. The space vacuum acts as
a cold source where energy is lost, mostly in the radiative form. Between cold sources
and warm sources, macroscopic motions occur spontaneously leading to convection cells.
They happen in the mantle, the oceans, and the atmosphere. Convection is just an
example of a macroscopic phenomenon that occurs spontaneously in open systems far
from thermodynamic equilibrium, and specifically on Earth. Another example is the
3
We put radioactive elements aside because radioactivity leads to the fission of atoms, thus their
destruction.

11
cycle of water, which involves state changes.
These various macroscopic phenomena can lead to the magnification of ore con-
centration, often as a result of a contingent combination of processes. For example,
heavy compounds tend to sink to the core of the Earth; however, melted magma rises
as a result of convection in the mantle. In magma chambers, gravitation leads heavier
elements to sink and thus to the appearance of heterogeneities. Later, the resulting
rocks can be submerged or exposed to rainwater, and some compounds will dissolve.
If the elements of interest dissolve, they may precipitate at a specific location where
appropriate physicochemical conditions are met, leading to an increased concentration.
Alternatively, some elements, for example, gold, may not dissolve in most situations,
but other compounds surrounding it may dissolve and be washed away, exposing gold
and increasing its local concentration. Then, gold nuggets can be transported by water
and concentrated further in specific places in streams — a key and iconic factor of the
American gold rush. In general, ore deposits are the result of such combinations of
processes (Heinrich and Candela, 2014; D.Scott et al., 2014).
In a nutshell, ore deposits are the result of macroscopic phenomena that occur
on Earth because it is far from thermodynamic equilibrium. Human activities take
advantage of this naturally occurring process and pursue it further by several industrial
methods that produce very high concentrations in the intended element. All these
processes require macroscopic work and generate entropy.

2.2.2 Wear and entropy

In the use of artifacts, wear can lead to the dispersion of the compounds of the objects
used. For example, the emission of fine particles from motor vehicles stems as much
from the wear of tires and breaks than from the combustion engines (Rogge et al., 1993).
The wear of mechanical components stems from the transformation of part of the
mechanical work into heat, leading to a production of entropy. Part of this entropy
is released on the surroundings as heat. Another part increases the entropy of the
component. Entropy production at the level of the elements of a machine is a general
framework to understand the wear caused by their use (Bryant et al., 2008; Amiri and
Khonsari, 2010). Similar phenomena occur in electronics and microelectronic. Elec-
tric currents increase the probability that atoms move in the components, leading to
higher entropy than in the designed configuration, and ultimately to component failure
(Basaran et al., 2003). A similar phenomenon also occurs in batteries and explains their
“aging” (Maher and Yazami, 2014).
Another compelling case is the appearance of microplastics at increasingly high lev-
els in seawater. The origin of these microplastics seems to be in the water of washing
machine when washing synthetic textiles (Browne et al., 2011). The resulting concen-
tration in the environment is sufficient to threaten wildlife (do Sul and Costa, 2014).
All these examples show that artifacts are altered over time because their use strains
them. Moreover, this alteration can result in particles that are dispersed in the sur-
roundings and threaten human and wildlife health. All these phenomena are entropy
increases.

2.2.3 Bioaccumulation, bioconcentration, biomagnification

Living beings, especially bacteria, can contribute to the formation of ore deposits by
their biochemical activities. However, there is another relevant extension of this dis-
cussion in the biological realm. Biotic processes can concentrate compounds released
in the environment by industrial processes and products. The accumulation of such

12
compounds in biological organisms impacts their survival and the safety of their con-
sumption by humans.
Several processes are involved in this phenomenon (Barron, 2003). The first is the
bioaccumulation from sediments. This process is very relevant for heavy compounds
that sink to the ocean floor, such as heavy metals or microplastics. It largely depends
on the behaviors of the organisms involved. Some of them, like worms, can ingest
relatively old sediments whereas other organisms feed at the surface of sediments.
The second process is the bioconcentration from compounds present in water. Some
compounds existing in water have a higher affinity with particular organs or tissues
than with water itself. As a result, even assuming that equilibrium between intake
and excretion of the said compound is reached, they are in higher concentration in
organisms than in water. For example, lipophilic and hydrophobic compounds such as
PCBs accumulate in fat tissues.
The bioaccumulation from sediments is made possible by the feeding activity of or-
ganisms, a process far from thermodynamic equilibrium. Similarly, bioconcentration
from water stems mostly from the fast chemical exchanges taking place during respi-
ration, at the level of gills for large organisms. In both cases, accumulation is made
possible by the specific chemical compositions of organisms. The latter are generated
and sustained by organisms — a process far from thermodynamic equilibrium. Depend-
ing on the cases, the concentration inside the organism can reach a balance between the
intake and release. On the opposite, organisms can collect compounds in their milieu
without reaching the equilibrium concentration.
The last relevant process is biomagnification in food chains. Living beings feed on
each other. Bioaccumulation from sediments and bioconcentration lead to the presence
of compounds in prey organisms. Then, these compounds become part of the food of
a predatory organism and can accumulate further in the latter. This process follows
the food chain magnifying the concentration of the compound that gets higher than
in sediments and water. The bioaccumulation of heavy metals and PCBs leads to
organisms that are improper for consumption.
In these examples, the concentration of metals and chemicals is increased dramat-
ically by biological processes. There is a reduction of the entropy of their spatial dis-
tribution. This process is detrimental to the biosphere in general and humankind in
particular.

2.2.4 Conclusion
There are geological processes that occur far from thermodynamic equilibrium. These
processes lead to a distribution of compounds that is far from what we would expect by
a straightforward application of the second principle of thermodynamics. Humankind
takes advantage of this situation and extract ores from deposits with sufficient concen-
trations, and concentrate them more by industrial processes. However, processes such as
the wear of artifacts also lead to the dispersion of various compounds in the biosphere.
The presence of these compounds at these concentrations is new from an evolution-
ary perspective, and there is no specific biological process stemming from evolution
that mitigates their consequences. Depending on their properties and the physiology
of the organisms exposed, they can lead to bioaccumulation, bioconcentration, and
biomagnification in the food chain. These processes lead to a high concentration of
several compounds at the worse possible locations for biodiversity and humankind: in
the body of organisms. In these cases, the decrease of the entropy corresponding to the
concentration of these compounds is detrimental.

13
2.3 Conclusion
In a nutshell, entropy describes the degradation of energy in physics. This degradation
means going from unlikely macrostates towards more likely macrostates, that is to say,
from specific configurations to more generic ones.
Defining entropy requires the articulation between microstates and macrostates.
Theoretical choices of macrostates are based on their causal role, and the latter depends
on the couplings with surroundings. Therefore entropy also depends on the nature of
these couplings. Moreover, available energy, exergy, depends not only on the nature of
the variables involved in these couplings but also on their values. Nevertheless, some
couplings and macroscopic descriptions are generic to a large extent for technological
purposes; for example, the mobility of persons and goods leads to analyze macroscopic
mechanical couplings.
In engineering, entropy typically comes into play to analyze the functioning of a
machine, starting historically with heat engines. However, the production of machines
also involves entropy, as exemplified by our discussion on mineral resources. This remark
connects with the biological concept of autopoiesis: an organism has to maintain or
regenerate its parts. The design of machines is also external to the analysis of functioning
machines, and the function of machines and artifacts can change depending on the user,
beyond generic analyses of their use. These ideas are reminiscent of biological evolution.
Taking all these aspects into account leads to a more biological view of technologies.
Ultimately, available energies (exergy) depends on a given technological apparatus, and
the problematic increases of entropy are relevant from the perspective of technological,
social, and biological organizations.

3 Entropy and organizations

Schrödinger (1944) emphasized that biological situations remain far from thermody-
namic equilibrium. There is no contradiction with the second principle of thermody-
namics because biological systems are open systems that can release entropy on their
surroundings. We already discussed macroscopic movements of matter on Earth that
occur spontaneously far from thermodynamic equilibrium and sometimes lead to the
formation of ore deposits, thus to low entropy configurations.
Schrödinger went further and proposed to analyze biological order as a negative en-
tropy. There are little doubts that biological organizations correspond to a low entropy
insofar as we can define their entropy. There have been several theoretical works along
this line (Nicolis and Prigogine, 1977; van Bertalanffy, 2001). However, conflating low
entropy and the concept of organization is not accurate. Everything that contributes to
the low entropy of biological situations is not relevant for their organizations. For ex-
ample, the growth of a cancerous tumor is an increase of morphological complexity, but
a decrease in organization (Longo et al., 2015). Similarly, we have discussed biomagnifi-
cation and other processes that reduce the entropy of chemicals spatial distribution but
are detrimental to biological organizations. Moreover, entropy is extensive; it is pro-
portional to the size of a system. By contrast, critical parts of a biological organization
may not amount to much quantitatively, such as a single nucleotide or a few molecules
in a cell.
This kind of shortcomings led to propose another quantity to address biological
organizations: anti-entropy (Bailly and Longo, 2009; Longo and Montévil, 2014a). Anti-
entropy was first a macroscopic extension of far from equilibrium thermodynamics. The
term anti-entropy stems from an analogy between the relation matter/anti-matter and

14
entropy/anti-entropy. Entropy and anti-entropy are similar, they have an opposite sign,
and at the same time, they have a qualitatively different meaning. They only “merge"
when the organism dies or, more generally, when an organization collapses.
To go further, we have to introduce several theoretical concepts designed to un-
derstand biological organizations and discuss their articulation with entropy. Then,
we will show that the nature of biological organizations leads to two specific kinds of
vulnerabilities to the changes of the Anthropocene.

3.1 Theoretical background

We first discuss couplings between biological organizations and their surroundings, pro-
vided that it is a crucial element in the definition of entropy. Then, we discuss the nature
of putative biological micro spaces and show that they lead to introduce the fundamen-
tal concept of historicity. Last, we address how organizations maintain themselves far
from thermodynamic equilibrium by the interdependencies between their parts.

3.1.1 Couplings with the surroundings

The couplings between a system and its surroundings are critical to defining entropy
and thermodynamic equilibrium, as discussed in section 2.1.2. However, in biology, the
couplings between organisms and their milieu is a far more complex theoretical notion.
First, biology requires to historicize the concept of coupling. Couplings change in
evolution and development. It is even tempting to consider specific principles (Kirchhoff
et al., 2018). Once living objects are exposed to phenomena that impact their orga-
nization, they will tend to establish couplings with these phenomena in a diversity of
ways. For example, some phenomena can be a source of free energy. It is the case of
light, which enabled photosynthetic processes. Similarly, humans have recently concen-
trated radioactive compounds for industrial purposes. In Chernobyl, Ukraine, wildlife
was exposed to these compounds, and fungi appeared that metabolize their intense
radiations (Dadachova et al., 2007). However, couplings are not limited to significant
sources of free energy. For example, light is also used by many organisms to perceive
their environments.
In these examples, the inside and the outside of an object are well-defined. How-
ever, the organisms’ surroundings are not just static. Instead, organisms change them
actively. With the ability to move, organisms can discover and secure different sur-
roundings. In the process of niche construction, they actively produce part of their sur-
roundings (Odling-Smee et al., 2003; Pocheville, 2010; Bertolotti and Magnani, 2017).
Beyond the concept of coupling between inside and outside, biology involves couplings
between different levels of organization. These couplings stem from a shared history, for
example, between a multicellular organism and its cells, and organisms and ecosystems
(Soto et al., 2008; Longo and Montévil, 2014b; Miquel and Hwang, 2016).
In a nutshell, physicists established thermodynamics for systems where the coupling
between a system and its surroundings is well defined and is usually static. This frame-
work enables engineers to control industrial processes and artifacts. By contrast, the
coupling between living organizations and their surroundings is not well defined. It
is not an invariant of the object. Current couplings are the result of natural history,
and continue to change, producing history (Miquel and Hwang, 2016; Montévil et al.,
2016). In ecosystems, the appearance of a species present many opportunities for new
couplings, that is to say, new possible niches (Longo et al., 2012; Gatti et al., 2018). We
can include social organizations and their production of artifacts in the discussion —
artifacts are analyzed as exosomatic organs by Lotka (1945). Then, living matter has

15
coupled some of its processes, the activity of physicists, to remarkably weak phenomena
at biological scales such as gravitational waves or interactions with neutrinos.
Couplings are far more proteiform in biology than in the standard framework of
thermodynamic. In the case of artifacts and industrial processes, let us recall that the
thermodynamic couplings correspond to the purpose of the said processes in order to
generate useful work. In this context, the plasticity of biological couplings corresponds
to the variability of biological functions that is intrinsic to the historical changes of
biological objects.

3.1.2 Micro spaces in biology

The situation for candidate micro spaces in biology differs from the basic hypotheses
used to define entropy.
First, space is materially broken down by membranes at all scales, from organelles
and cells to tissues, organs, and organisms. This spatial organization restricts diffusion
and the rate of entropy increase. In turn, this partial compartmentation ensures that
for many kinds of molecules, the number of molecules remains small in compartments
such as cells. Chromosomes, in particular, exist in only a few copies in each cell. We
have seen with the example of coin throwing that a macroscopic variable was stable in
the case of a high number of throws but highly random for a small number of throws.
It is the same for molecular processes in cells, and the low number of molecules leads
to randomness (Kupiec, 1983; Kaern et al., 2005; Corre et al., 2014). This randomness,
in turn, implies that the deterministic picture for collections of molecules in cells is not
sound (Lestas et al., 2010).
Second, the complexity of cellular proteomes includes networks of numerous com-
pounds interacting and exhibiting complex dynamics (Kauffman, 1993; Balleza et al.,
2008). To an extent, these dynamics can even “improvise” when, for example, the reg-
ulation of a gene’s expression is artificially jammed (David et al., 2013; Braun, 2015).
Last, the nature of the molecules existing in cells and organisms is not a theoretical
invariant. As a result, we have to take into account the changes in the relevant molecules.
For example, proteins are chains of amino acids. If we consider only proteins with 200
amino acids, there are 22200 possible molecules. This number is gigantic: if all the
particles of the universe (1080 ) were devoted to exploring this space of possibility by
changing at the Planck time scale, they would not manage to explore much of this
space in the universe lifetime (Longo et al., 2012). Unlike Boltzmann, we cannot build
on the idea that microscopic possibilities would be explored uniformly, leading towards
generic configurations (the most probable macrostate). Instead, we have to focus on
how systems explore possibilities in a historical process.
If the difficulty were limited to this aspect, it would not genuinely hinder the use
of mathematical reasoning to find generic patterns. For example, mutations without
selection (neutral mutations) lead to a random walk in the space of possible dna se-
quences, and probability distributions describe this process well. Its generic properties
are used to assess the genealogical proximity of different species. Similarly, we can ana-
lyze the generic properties of large networks of interacting molecules if the interactions
are generic; i.e., all have the same nature.
The problem is that this process leads to molecules with qualitatively different behav-
iors. For example, molecular motors or tubulin do very different things than enzymes.
Molecular motors are molecules that “crawl” on macromolecular structures and tubulin
are molecules that constitute fibers spontaneously. Moreover, molecules contribute to
macroscopic structures and interact with them. In this process, their biological mean-

16
ings acquire qualitative differences. For example, crystallin proteins contribute to the
mechanical integrity of the eye, and they are transparent so that they do not hinder the
flow of light.
In the relevant organic and ecosystemic contexts, the specific properties of proteins
impact the process of exploration of dna sequences. As a result, the latter differs from a
random walk, and its determinants are multiple. Even the dynamic of neutral mutations
changes because the way mutations occur, can be inverted or prevented, and the process
of reproduction do change.
We consider how living beings live as the central interest of biology. Therefore,
functionally relevant changes are fundamental. In the case of mutations, biologically
relevant variations are the one that impacts biological organizations in one way or
another. When we discuss the primary structure of proteins (their sequence) or dna
sequences, we consider combinations of elementary elements, like a text is a combination
of letters and other symbols. If we take this process of construction alone, all combina-
tions seem equivalent, which wrongly suggests an analogy with Boltzmann’s hypothesis
of molecular chaos. In biology, these combinations are not biologically equivalent. They
can lead to qualitative novelties and changes in the exploration of these combinatorial
possibilities. In a nutshell, not only is the space of combinatorial possibilities massive,
but the "rules" of the exploration of this space depend on positions in this space —
and these positions are not the sole determinants. These rules are as diverse as func-
tional biological processes are, and thus are not generic (Montévil et al., 2016; Montévil,
2019b).
The epistemological and theoretical consequences of this situation are far-reaching,
and there is no consensus on the appropriate methods and concepts to accommodate
them (Bich and Bocchi, 2012; Montévil et al., 2016; Longo, 2018; Kauffman, 2019).
We have proposed to invert the epistemic strategy of physics. Physics understand
changes by invariance: the equation and their invariants describe changes of states but
do not change themselves. By contrast, in biology, we argue that variations come first,
and that (historicized) invariants come second. We call the latter "constraints" (Soto
et al., 2016; Montévil, 2019c). We have argued that, unlike in the theories of physics,
the definition of concrete experiments always has an essentially historical component in
biology. In physics, experiments can be performed de novo, whereas biological exper-
iments and their reproducibility rely on objects having a common origin, thus on the
ability of organisms and cells to reproduce (Montévil, 2019a).
In particular, the space of possibilities cannot be pre-stated both at the microscopic
and macroscopic levels — provided that stating possibilities requires to state their causal
structure explicitly. For example, the space generated by molecular combinatorics is
not genuinely a space of possibilities. It is not endowed with a proper causal structure
able to state explicitly that molecules like molecular motors or tubulin are possible.
Moreover, this space is far from complete, for example, proteins longer than 200 amino
acids exist, and proteins can recruit other elements such as iron in hemoglobin or iodine
in thyroid hormones. Nevertheless, this space is relevant: it is a space of possible
combinations of amino acids. This space is generated mathematically by the enzymes
defining the processes of transcription and translation (Montévil, 2019b). However, this
theoretical construct is insufficient to state the possible roles of the said combinations
in biological organisms. In this regard, possibility spaces in biology are not just a way
to accommodate changes; they are part of biological changes and are co-constructed by
them.

17
3.1.3 Persisting organizations
Several theoretical biologists have developed the idea that the parts of a biological
organization maintain each other (Varela et al., 1974; Rosen, 1991; Kauffman, 1993;
Letelier et al., 2003). In particular, Kauffman (2002) articulates constraints and work
in the thermodynamic sense. In Kauffman’s schema, work maintains constraints and
constraints canalyze work. This interdependency leads to the persistence of work and
constraints as long as the surroundings allow it.
We have developed a general and formalized framework describing the interplay
between processes of transformations and constraints. In this framework, a constraint
is invariant w.r. to a process, at a given time scale, but it canalyzes this process. A
constraint C1 can act on a process that maintains another constraint C2 . Then, we say
that C2 depends on C1 . We hypothesized that relations of dependence in organizations
lead to cycles. For example, C1 depends on C2 , C2 depends on C3 , and C3 depends on
C1 (Montévil and Mossio, 2015; Mossio et al., 2016). We call this kind of circularity
closure of constraints.
Closure of constraints is very different from being closed in the thermodynamic
sense. Organizations depend on flows from the surroundings at the level of processes
to remain far from thermodynamic equilibrium. For example, mammals depend on
food and oxygen flows. They also depend on external constraints that are necessary to
sustain internal constraints but are not maintained by the closure. For example, many
organizations depend on the physical periodicity of night/day cycles.
Constraints are not necessarily macroscopic (and thus thermodynamic). Constraints
are patterns structuring processes of transformation; they can exist at all space and
time scales. For example, dna sequences are constraints on gene expression. Dna
3D configurations influence the accessibility of genes and are also constraints on gene
expression. Similarly, the geometry of the vascular system is a constraint on blood flow
in tetrapods.
In this framework, biological entities maintain their configuration far from thermo-
dynamic equilibrium in a distinct way. Let us recall that, in physics, a configuration
far from thermodynamic equilibrium can appear and persist by the self-organization of
flows stemming from their surroundings. It is the case in convection cells, for example.
Biological organizations last for different reasons. In the framework of the closure of
constraints, organizations persist thanks to the circular interdependencies between con-
straints. They are not the result of spontaneous self-organization of flows (Longo et al.,
2015).
Organizations are not spontaneous also in the sense that they stem from history. Self-
organization in physics is generic; for example, convection cells always follow the same
pattern at the right level of analysis. By contrast, closure of constraints is compatible
with many qualitatively different configurations. For example, different bacteria can live
in the same milieu. Reciprocally, in the historicized epistemological framework that we
have hinted to, invariants (constraints) cannot be postulated like in physics, they require
an explanation. Closure of constraints is a way to explain the relative persistence of
some constraints (Montévil et al., 2016; Mossio et al., 2016; Montévil, 2019c). Natural
selection is another, complementary way to explain the relative stability of constraints.
Closure of constraints describes constraints collectively stabilizing each other. It
does not follow, however, that the constraints of an organization remain static. On
the opposite, there are limits to the stability of biological organizations. For example,
intrinsic variations follow from the small number of most molecules in cells (Lestas
et al., 2010). As a further illustration, let us consider a gene coding for a fluorescent

18
protein, but with a mutation preventing the formation of the said protein if the code is
considered exact. However, it is not exact. Randomness in gene expression generates
a diversity of variants, including the fluorescent protein, and bacteria presenting the
mutated gene will be fluorescent (Meyerovich et al., 2010).
Actual biological organizations result from the iterative integration of novelties. Nov-
elties are random in the sense that they cannot be predicted from the current state of
affairs; however, they are not generic; as discussed above, they provide a specific con-
tribution to organizations. Specificity stems both from the structure of constraints and
their articulation to an organization.

3.1.4 Conclusion
In order to specify anti-entropy further, we propose to consider that an element relevant
for anti-entropy satisfies three criteria. i) It contributes to organization sensu closure
of constraints; informally, it has a systemic role in the persistence of the organism. ii)
It is the specific result of history. iii) The specific properties in (ii) are the condition for
the systemic role in (i).
It follows from this definition that anti-entropy is relative to an organization. A
change that increases the anti-entropy of an organization can reduce the anti-entropy
of another and even lead to its complete collapse.
There are two ways in which anti-entropy can be nonconservative. First, it can
decrease, which leads to the production of entropy, the ultimate example being death.
Second, by analogy with entropy production, we propose the concept of production of
anti-entropy. Anti-entropy production corresponds to the appearance of novelties, as
described above. This process is time-oriented, like entropy production.
There are processes in biology that are analyzed as physical self-organization, such
as convection cells or Turing’s morphogenesis (Turing, 1952). According to our defini-
tion, they do not contribute per se to anti-entropy: they are generic. However, their
conditions of possibility and their role in other processes, such as cellular differentiation,
can be relevant for anti-entropy. In the latter case, they are enabling constraints for
the growth of anti-entropy. Here, we are following a line of reasoning similar to van
Bertalanffy (2001). He distinguishes mechanized processes that lead consistently to a
given result at the level of the parts and non-mechanized processes that involve the
organism as such.
Last, anti-entropy production requires to produce a specific situation conveying a
specific biological meaning. Such situations are not generic outcomes; therefore, they
require work of exploration that can be either at the level of the new parts or by broader
changes of organization. This exploration can be either at the level of an individual, a
group, a population, or an ecosystem. In the particular case of humans, this exploration
can be performed by intellectual work to an extent, using tools such as pens and papers
or computers.

3.2 Disruptions as entropizations of anti-entropy

We will now discuss how this framework can contribute to understanding the Anthro-
pocene crisis. Let us start with an example.
Seasonal variations constrain living beings and their activities. Biological responses
specific to this rhythm appeared in evolution. The internalization of seasonal rhythms
is an example of the trend to establish complex couplings that living beings exhibit,
as discussed above. Many biological events such as blooms, hatching, and migrations

19
 Pollinator Pollinator

Plant
Plant
Plant

Figure 3: Phenological differences between plants and pollinators after a change of cli-
mate (adapted from Jane et al., 2007). Left, situation before the change. The pollinator
is viable because there are plants that flower during all its activity period. Right, sit-
uation after climate change. The activity periods changed somewhat randomly. The
pollinator has two parts of its activity period without a plant to pollinate which leads
to its disappearance in the model.

take place at specific times of the year. The study of periodic events in the living world
associated with seasonality is phenology.
In ecology, the “desynchronizations" of activities in an ecosystem can break down
relations between populations in an ecosystem. These alterations and their consequences
are often called disruption, and their study is a particularly active field of research. They
are relevant economically, socially, and for conservation biology (Morellato et al., 2016;
Stevenson et al., 2015).
We argue that understanding these disruptions supposes simultaneously to analyze
i) the relations in a system and ii) the natural history which originates a specific syn-
chronization iii) that contributes to the populations’ viability. In other words, we think
that disruptions decrease anti-entropy.
Let us describe the typical situation in more detail. If all populations would follow
the same shift, then there would be no change in their interactions. However, species
use a diversity of clues to articulate their behavior with seasons (called Zeitgeber, e.g.,
temperature, snow, soil temperature, and photoperiod Visser et al., 2010). The impact
of climate changes on phenologies is diverse, because, for example, climate change does
not impact photoperiods but does impact temperatures. The diversity in phenological
changes impacts the possible interactions and can destabilize ecosystems.
For example, Jane et al. (2007) modeled the disruption of plant-pollinator interac-
tions in an ecosystem. In this model, the notion of disruption has a precise meaning,
which is not discussed by the authors. Let us describe their model. Each plant has a
flowering period, and each pollinator has a period of activity. Plant-pollinator interac-
tions stem from empirical data. A plant has to be pollinated by at least one pollinator
to reproduce. A pollinator must have plants to pollinate during its whole period of
activity to survive.
The outcome of this computational model is that few plants are vulnerable to the
change, but many pollinators are. Plants are relatively robust because, during their
flowering period, a single pollination event is sufficient for their survival. However,
pollinators are vulnerable because they need to feed during their whole period of activity,
see figure 3.
What happens in this model at a deeper theoretical level? The initial situation is in
a small part of the space of possible activity periods because all plants and pollinators
are in a viable configuration. The underlying history of these ecosystems explains that
these particular configurations exist. The condition of viability for plants and pollinators

20
leads to a systemic analysis of their networks of interactions, at a given time. After a
change in the local climate and the subsequent, diverse phenological offsets, a significant
number of pollinators and some plants are no longer in a viable configuration. Here,
the specific initial situation transforms into a more random or "arbitrary" configuration
concerning the viability and Natural History. In this model, disruption is the dissipation
of the result of history impacting the sustainability of systems parts.
The initial situation contributes to anti-entropy. The elements of the system con-
tribute to their viability by plant-pollinator interactions (i). The initial configuration is
specific because it is in a small part of the possibility space as a result of natural history
(ii). Last, this specific configuration has an organizational meaning: in our example, all
populations are viable because of them (iii). The initial configuration meets our three
criteria; therefore, the specificity of the initial configuration is part of the anti-entropy
of the ecosystem.
The final configuration is more generic than the initial one; it is more random con-
cerning viability criteria. Climate change leads to the loss of part of the anti-entropy
by the process of entropy increase in the space of activity periods.
There are many situations were similar reasonings take place to analyze disruptions
of synchronicities, even though our theoretical interpretation is not explicitly used (for
example, Robbirt et al., 2014; Rafferty et al., 2015; Jane et al., 2007).
Our discussion in terms of anti-entropy and its decrease in disruption is more general
than the case of seasonal synchronicities. Climate change and other changes of the
Anthropocene disperse part of the anti-entropy of biological organizations and produce
entropy at the level of the relevant description space. The configuration after the change
occupies a larger part of the description space than initially, and these configurations
do not fit with the organization of the system (in our example, not all populations are
viable).
Biological organizations have a particular vulnerability. They build on regularities,
in particular, the ones in their surroundings. However, these regularities can change, and
in the Anthropocene, they change very quickly as a result of human activities. In many
cases, unlike in cybernetics, no feedback stabilizes these couplings, at least not on short
time scales. When the surroundings change, fine-tuned organization become randomized
and thus disorganized to an extent. A similar phenomenon occurs, for example, in the
case of endocrine disruptors. Chemical industries produce new chemicals, some of which
interfere with hormone action. Since these chemicals and family of chemicals are new
occurrences in the biosphere, there is no organized response to them, and they tend to
randomize hormone action. Endocrine disruptors lead to many adverse effects, both for
human and wildlife (Zoeller et al., 2012).
We thus have a first organizational concept for the Anthropocene crisis: a partial
loss of anti-entropy that corresponds to an increase of entropy. Here, entropy is not
directly the concept of physics (i.e., with kb ): the growth of entropy occurs for biological
quantities relevant for biological organizations. The loss of anti-entropy is the loss
of specific results of history contributing to the current organization of organisms or
ecosystems, leading to their disorganization.

3.3 The disruption of anti-entropy production

To introduce the last idea, let us start with examples from human activities.
Translations provide a simple, compelling example. Let us compare part of a recipe
of Bourguignon beef with the text after multiple translations by Google Translate.
Translations were performed from English to Arabic, to Hindi, to Gaelic, to Chinese

21
(traditional), to Russian and back to English.

Original text Text after translation

1) Cut bacon into 1/4 inch thick pieces. 1) Cut the bacon into 1/4 inch slices.
Simmer bacon for 10 minutes in water. Bacon is boiled in water for 10 minutes.
Drain and pat dry. Meanwhile, pre- Moisten and let it dry. At the same
heat oven to 450 degrees. time, preheat the oven to 450 degrees.
2) In a large casserole pot, saute bacon 2) In a large saucepan, bake olive oil
in olive oil on moderate heat for about over low heat for 2-3 minutes, until it
2-3 minutes to brown lightly. When turns slightly brown. When ready, put
ready, reserve bacon to a side dish. the bacon in the side dish.
3) Pat dry the cubed beef with paper 3) Dry the chopped beef in a bowl
towels and brown in olive oil in the with paper towels and brown olive oil.
same pot. Brown on all sides. Only Brown from all sides. Just fold it once
do one layer at a time, so don’t over- to avoid folding the pot. When done,
crowd the pot. Reserve meat to a plate store the meat on a plate.
when done.

The outcome is sometimes accurate, sometimes involves a loss of accuracy, and is

occasionally meaningless or wrong. It is worth noting that technical terms such as
“simmer” or “reserve” vanished.
What happened in this process? Google translate uses a Neural Machine Translation
System that builds on preexisting translations to find statistical patterns (Wu et al.,
2016). However, these statistical patterns do not always preserve meaning. A good
translator does not just rely on usual ways to translate words and sentences but strives
to convey meaning in another language. Here, conveying meaning is a practical notion; it
means to enable the reader to perform the recipe. Since cooking methods and ingredients
are specific to a locality, translating a recipe should not be literal; the translated text
has to find its home in a different gastronomic culture.
There are many ways to convey meaning in translation. For example, the translator
may choose not to translate a word but to define it instead. The recipe used here is
itself a "human" translation from the french. However, in french, “reserve bacon to a
side dish” is redundant because “réserver” means to keep aside for later use; this is
an implicit definition. Similarly, translating ingredients is a very complex operation
because it involves substitutions. Ultimately, sometimes, the only way to translate a
recipe correctly involves tests to reproduce it in a given locality. The meaning of recipes
stems from the coupling between a food production and distribution apparatus, and a
culture of culinary techniques.
To convey the meaning of a text, good translators often need to depart from the text
and a fortioti from its statistical translation. The statistical translations are the ones
that maximize entropy, at least in a conceptual sense (sometimes in the technical sense of
information theory), because they are the most probable output once we have a database
of known translations. In other words, the automatic translations are the ones that fit
the most closely to preexisting patterns. By contrast, the departing from the most
probable translations by a good translator involves the choice of an unlikely translation
to convey meaning. This notion fits our concept of novelty (Montévil, 2019b), thus
corresponds to the concept of anti-entropy production transposed at the linguistic and
gastronomic interface — let us recall that, here, cooking tests are part of the translator
tools: translation is never just a linguistic problem.

22
 In a nutshell, the preservation of meaning in translation often requires the introduc-
tion of novelties in the translation, akin to the production of biological anti-entropy.
Like biological novelties, they are unlikely and, at the same time, convey a specific
meaning. By contrast, the use of automatic statistical translations leads to a more
or less significant loss of meaning because of its inability to introduce such novelties.
In this perspective, translators do not optimize the transmission of information sensu
Shannon (1948); instead, they add information to preserve the initial meaning.
Another interesting example is the interaction between infants and digital media.
This interaction does not provide benefits and can be detrimental to children (Brown
and et al, 2011). Let us quote part of the explanation given by Marcelli et al. (2018).

The sequences presented to toddlers on screens have a double effect: the

"show" in perpetual motion captures their eyes, but this capture takes place
without any interactive synchrony with what these toddlers can feel, under-
stand, live, experience, etc.
They are passive and submissive spectators who go through the scenario and
hear a "mechanical" voice, which, most often, makes them silent. Because
there is no prosodic synchronization possible, the toddler remains silent ...
[...] this flow of stimulation leaves the toddler in front of an attractive enigma
but one that is difficult to understand. (Marcelli et al. 2018, we translate)

In a nutshell, young children are not able to follow a narrative by themselves. Parents
“cheat” and adjust their proto-narrative to their children’s behavior in order for this
proto–narrative to make sense for the child. In other words, the parents constitute
meaning artificially by improvisations based on infant reactions. This activity does not
exist in the case of digital media, where the unfolding of the scenario is generic.
In both the case of translators and parents, we see that the ability to generate
novelties is critical in order to convey or generate meaning. Here, novelties contribute
to a specific meaning and are, at the same time, unlikely. They can be improbable but
may also not even be possible in a positive sense. For example, words outside of the
dictionary can be used, such as untranslated words or neologisms. In the use of current
algorithms, the ability to generate such novelties disappears.
Are there similar phenomena in strictly biological situations? Templeton et al. (2001)
raise the issue of the disruption of evolution, and more specifically of the process of
adaptation by natural selection. If a population is fragmented, the gene flows between
the different fragments stop, and the evolutionary processes will take place in each
fragment independently. The population relevant to the evolutionary analysis shrinks
from the initial population to the population of each fragment. Then the nature of
the evolutionary dynamics changes. It becomes dominated by genetic drift, and each
subpopulation’s genetic diversity will decrease. The process of natural selection will not
have enough diversity for differential reproduction to lead to adaptations. Empirical
results support this analysis (Williams et al., 2003). Here, by contrast with the previous
section, it is not only the result of a history that is the object of the disruption but also
the ability to produce a history. The ability to produce anti-entropy by the process of
natural selection is disrupted.

4 Conclusion
The concept of entropy requires rigorous reasoning; otherwise, it leads to significant
mistakes. Entropy is a reliable concept in equilibrium thermodynamics. Since the

23
concept of usable energy depends on the couplings with a system’s surroundings, and
these couplings can be diverse to study the life cycle of a given artifact, it would make
little sense to perform a straightforward accounting of physical entropy.
Non-equilibrium thermodynamics and theoretical biology are far from being as the-
oretically stable as equilibrium thermodynamics. Nevertheless, there are definite situ-
ations. Earth is an open system, where geological processes contingently magnify the
concentration of elements leading to ore deposits formation. Once purified and used
to construct artifacts, the use of these artifacts tends to disperse these resources back
in the environment. It is especially the case in tire and breaks wear. Organisms may
concentrate them again, with adverse consequences for both humankind and wildlife.
Processes leading to the increase in the concentration of elements are associated with
a cost in free energy in one form or another, they can happen spontaneously because
Earth and the biosphere are far from thermodynamic equilibrium and are open to fluxes
of energy.
The concept of entropy and its derivatives are necessary to address these phenomena
and the notion of “consuming energy” and “consuming mineral resources”. The core
of this conceptual point is that, in both cases, configurations matter more than mere
quantities. However, physical analyses are limited to the functioning of a machine or a
given step in its production. However, what genuinely matters is their articulation with
given biological, technological, and social organizations.
In biology, we have emphasized the centrality of organizations and their historical
dimension. They lead to the concepts of anti-entropy and anti-entropy production.
Anti-entropy corresponds to relevant parts of an organization that are the specific result
of history, and perform a role in organizations because of that. Anti-entropy production
is the appearance of a novelty in a strong sense: an outcome that was initially improbable
or even unprestatable, and that provides a specific contribution to the organization. It
follows that both concepts are relative to a given organization.
These two concepts lead to two kinds of disruption of biological and human organiza-
tions. In the disruption of anti-entropy, changes lead to the loss of specific configurations
associated with a specific role in organizations. In other words, part of anti-entropy is
lost in favor of more random configurations w.r. to the biological organization. This
phenomenon is the entropization of part of anti-entropy.
The disruption of anti-entropy production is the loss of the ability to generate nov-
elties contributing to biological organizations. In the human examples discussed, the
ability to produce specific texts or interactions conveying meaning is disrupted by the
use of digital media.
Overall, this investigation shows that the concept of entropy is critical to under-
stand the Anthropocene; however, its specific role ultimately depends on the analysis
of relevant physical processes and biological or social organizations.

Acknowledgments
This work has received funding from the MSCA-RISE programme under grant agree-
ment No 777707 and the Cogito Foundation, grant 19-111-R. We thank Giuseppe Longo,
Jean-Claude Englebert and the IRI Team for comments on previous versions of this
manuscript.

24
References
Amiri, M. and M. M. Khonsari (2010). On the thermodynamics of friction and weara
review. Entropy, 12(5):1021–1049. ISSN 1099-4300. doi: 10.3390/e12051021.

Ayres, R. U. (1999). The second law, the fourth law, recycling and limits to growth. Eco-
logical Economics, 29(3):473 – 483. ISSN 0921-8009. doi: 10.1016/S0921-8009(98)
00098-6.

Bailly, F. and G. Longo (2009). Biological organization and anti-entropy. Journal of

Biological Systems, 17(1):63–96. doi: 10.1142/S0218339009002715.

Balleza, E., E. R. Alvarez-Buylla, A. Chaos, S. Kauffman, I. Shmulevich, and M. Al-

dana (2008). Critical dynamics in genetic regulatory networks: Examples from four
kingdoms. PLoS ONE, 3(6):e2456. doi: 10.1371/journal.pone.0002456.

Barron, M. G. (2003). Bioaccumulation and bioconcentration in aquatic organisms.

In D. J. Hoffman, B. A. Rattner, G. A. B. Jr., and J. C. Jr., editors, Handbook of
Ecotoxicology, pages 877–892. Lewis Publishers, Boca Raton, Florida.

Basaran, C., M. Lin, and H. Ye (2003). A thermodynamic model for electrical current
induced damage. International Journal of Solids and Structures, 40(26):7315 – 7327.
ISSN 0020-7683. doi: 10.1016/j.ijsolstr.2003.08.018.

van Bertalanffy, L. (2001). General system theory: Foundations, development, applica-

tions. Braziller.

Bertolotti, T. and L. Magnani (2017). Theoretical considerations on cognitive niche

construction. Synthese, 194(12):4757–4779. ISSN 1573-0964. doi: 10.1007/
s11229-016-1165-2.

Bich, L. and G. Bocchi (2012). Emergent processes as generation of discontinuities.

In Methods, models, simulations and approaches towards a general theory of change.,
pages 135–146. World Scientific, Singapore. doi: 10.1142/9789814383332_0009.

Braun, E. (2015). The unforeseen challenge: from genotype-to-phenotype in cell popu-

lations. Reports on Progress in Physics, 78(3):036602. doi: 10.1088/0034-4885/78/
3/036602.

Brown, A. and et al (2011). Media use by children younger than 2 years. Pediatrics,
128(5):1040–1045. ISSN 0031-4005. doi: 10.1542/peds.2011-1753.

Browne, M. A., P. Crump, S. J. Niven, E. Teuten, A. Tonkin, T. Galloway, et al.

(2011). Accumulation of microplastic on shorelines woldwide: Sources and sinks.
Environmental Science & Technology, 45(21):9175–9179. doi: 10.1021/es201811s.
PMID: 21894925.

Bryant, M., M. Khonsari, and F. Ling (2008). On the thermodynamics of degradation.

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences,
464(2096):2001–2014. doi: 10.1098/rspa.2007.0371.

Buonsante, P., R. Franzosi, and A. Smerzi (2016). On the dispute between boltzmann
and gibbs entropy. Annals of Physics, 375:414 – 434. ISSN 0003-4916. doi: 10.1016/
j.aop.2016.10.017.

25
Chibbaro, S., L. Rondoni, and A. Vulpiani (2014). Reductionism, Emergence and levels
of reality. Springer. ISBN 978-3-319-06361-4. doi: 10.1007/978-3-319-06361-4.

Corre, G., D. Stockholm, O. Arnaud, G. Kaneko, J. Viñuelas, Y. Yamagata, et al.

(2014). Stochastic fluctuations and distributed control of gene expression impact
cellular memory. PLOS ONE, 9(12):1–22. doi: 10.1371/journal.pone.0115574.

Dadachova, E., R. A. Bryan, X. Huang, T. Moadel, A. D. Schweitzer, P. Aisen, et al.

(2007). Ionizing radiation changes the electronic properties of melanin and enhances
the growth of melanized fungi. PLOS ONE, 2(5):1–13. doi: 10.1371/journal.pone.
0000457.

David, L., Y. Ben-Harosh, E. Stolovicki, L. S. Moore, M. Nguyen, R. Tamse, et al.

(2013). Multiple genomic changes associated with reorganization of gene regulation
and adaptation in yeast. Molecular Biology and Evolution, 30(7):1514–1526. doi: 10.
1093/molbev/mst071.

Davis, J., A. A. Moulton, L. Van Sant, and B. Williams (2019). Anthropocene, cap-
italocene, plantationocene?: A manifesto for ecological justice in an age of global
crises. Geography Compass, 13(5):e12438. doi: 10.1111/gec3.12438. E12438 GECO-
1180.R1.

D.Scott, S., H. D. Holland, and K. K. Turekian, editors (2014). Geochemistry of Mineral

Deposits, Treatise on Geochemistry, volume 13. Elsevier, Oxford, 2 edition. ISBN
978-0-08-098300-4.

Gatti, R. C., B. Fath, W. Hordijk, S. Kauffman, and R. Ulanowicz (2018). Niche

emergence as an autocatalytic process in the evolution of ecosystems. Journal of
Theoretical Biology, 454:110 – 117. ISSN 0022-5193. doi: 10.1016/j.jtbi.2018.05.
038.

Gayon, J. and M. Montévil (2017). Repetition and Reversibility in Evolution: Theoretical

Population Genetics, pages 275–314. Springer International Publishing, Cham. ISBN
978-3-319-53725-2. doi: 10.1007/978-3-319-53725-2_13.

Georgescu-Roegen, N. (1993). The entropy law and the economic problem. In Valuing
the Earth: Economics, ecology, ethics, pages 75–88. MIT Press Cambridge, MA.

Goldstein, S., J. L. Lebowitz, R. Tumulka, and N. Zanghi (2019). Gibbs and boltzmann
entropy in classical and quantum mechanics. arXiv preprint arXiv:1903.11870.

Haraway, D. (2015). Anthropocene, Capitalocene, Plantationocene, Chthulucene: Mak-

ing Kin. Environmental Humanities, 6(1):159–165. ISSN 2201-1919. doi: 10.1215/
22011919-3615934.

Heinrich, C. and P. Candela (2014). Fluids and Ore Formation in the Earth’s Crust,
Treatise on Geochemistry, volume 13: Geochemistry of Mineral Deposits, chapter 1,
pages 1 – 28. Elsevier, Oxford, 2 edition. ISBN 978-0-08-098300-4. doi: 10.1016/
B978-0-08-095975-7.01101-3.

Jane, M., C. P. G., W. N. M., and P. M. V. (2007). Global warming and the disrup-
tion of plantpollinator interactions. Ecology Letters, 10(8):710–717. doi: 10.1111/j.
1461-0248.2007.01061.x.

26
Kaern, M., T. C. Elston, W. J. Blake, and J. J. Collins (2005). Stochasticity in gene
expression: from theories to phenotypes. Nature Reviews Genetics, 6(6):451–464.
doi: 10.1038/nrg1615.

Kauffman, S. (2002). Investigations. Oxford University Press, USA, New York. ISBN
9780195121056.

Kauffman, S. A. (1993). The origins of order: Self organization and selection in evolu-
tion. Oxford University Press, New York.

Kauffman, S. A. (2019). A World Beyond Physics: The Emergence and Evolution of

Life. Oxford University Press, New York.

Kirchhoff, M., T. Parr, E. Palacios, K. Friston, and J. Kiverstein (2018). The markov
blankets of life: autonomy, active inference and the free energy principle. Journal of
The Royal Society Interface, 15(138):20170792. doi: 10.1098/rsif.2017.0792.

Kupiec, J. (1983). A probabilistic theory of cell differentiation, embryonic mortality

and dna c-value paradox. Specul. Sci. Techno., 6:471–478.

Lestas, I., G. Vinnicombe, and J. Paulsson (2010). Fundamental limits on the suppres-
sion of molecular fluctuations. Nature, 467:174 EP –. doi: 10.1038/nature09333.

Letelier, J. C., G. Marin, and J. Mpodozis (2003). Autopoietic and (m,r) systems.
Journal of Theoretical Biology, 222(2):261 – 272. ISSN 0022-5193. doi: 10.1016/
S0022-5193(03)00034-1.

Longo, G. (2018). How future depends on past and rare events in systems of life. Founda-
tions of Science, 23(3):443–474. ISSN 1572-8471. doi: 10.1007/s10699-017-9535-x.

Longo, G., M. Montevil, C. Sonnenschein, and A. M. Soto (2015). In search of principles

for a theory of organisms. Journal of biosciences, 40(5):955–968. ISSN 0973-7138.
doi: 10.1007/s12038-015-9574-9. 26648040[pmid].

Longo, G. and M. Montévil (2014a). Biological order as a consequence of randomness:

Anti-entropy and symmetry changes. In Perspectives on Organisms, Lecture Notes in
Morphogenesis, pages 215–248. Springer Berlin Heidelberg. ISBN 978-3-642-35937-8.
doi: 10.1007/978-3-642-35938-5_9.

Longo, G. and M. Montévil (2014b). Perspectives on Organisms: Biological time, sym-

metries and singularities. Lecture Notes in Morphogenesis. Springer, Heidelberg.
ISBN 978-3-642-35937-8. doi: 10.1007/978-3-642-35938-5.

Longo, G., M. Montévil, and S. Kauffman (2012). No entailing laws, but enablement in
the evolution of the biosphere. In Genetic and Evolutionary Computation Conference.
GECCO12, ACM, New York, NY, USA. doi: 10.1145/2330784.2330946.

Lotka, A. J. (1945). The law of evolution as a maximal principle. Human Biology,

17(3):167–194.

Maher, K. and R. Yazami (2014). A study of lithium ion batteries cycle aging by
thermodynamics techniques. Journal of Power Sources, 247:527 – 533. ISSN 0378-
7753. doi: 10.1016/j.jpowsour.2013.08.053.

27
Marcelli, D., M.-C. Bossière, and A.-L. Ducanda (2018). Plaidoyer pour un nouveau
syndrome ń exposition précoce et excessive aux écrans ż (epee). Enfances & Psy,
79(3):142–160. doi: 10.3917/ep.079.0142.

Meyerovich, M., G. Mamou, and S. Ben-Yehuda (2010). Visualizing high error levels
during gene expression in living bacterial cells. Proceedings of the National Academy
of Sciences of the United States of America, 107(25):11543–11548. ISSN 1091-6490.
doi: 10.1073/pnas.0912989107. PMC2895060[pmcid].

Miquel, P.-A. and S.-Y. Hwang (2016). From physical to biological individuation.
Progress in Biophysics and Molecular Biology, 122(1):51 – 57. ISSN 0079-6107.
doi: 10.1016/j.pbiomolbio.2016.07.002.

Montévil, M. (2019a). Measurement in biology is methodized by theory. Biology &

Philosophy, 34(3):35. ISSN 1572-8404. doi: 10.1007/s10539-019-9687-x.

Montévil, M. (2019b). Possibility spaces and the notion of novelty: from mu-
sic to biology. Synthese, 196(11):4555–4581. ISSN 1573-0964. doi: 10.1007/
s11229-017-1668-5.

Montévil, M. (2019c). Which first principles for mathematical modelling in biology?

Rendiconti di Matematica e delle sue Applicazioni, 40:177–189.

Montévil, M. and M. Mossio (2015). Biological organisation as closure of constraints.

Journal of Theoretical Biology, 372:179 – 191. ISSN 0022-5193. doi: 10.1016/j.
jtbi.2015.02.029.

Montévil, M., M. Mossio, A. Pocheville, and G. Longo (2016). Theoretical principles

for biology: Variation. Progress in Biophysics and Molecular Biology, 122(1):36 – 50.
ISSN 0079-6107. doi: 10.1016/j.pbiomolbio.2016.08.005.

Moore, J. W., editor (2016). Anthropocene or Capitalocene? Nature, History, and the
Crisis of Capitalism. PM Press.

Mora, T. and W. Bialek (2011). Are biological systems poised at criticality?

Journal of Statistical Physics, 144:268–302. ISSN 0022-4715. doi: 10.1007/
s10955-011-0229-4.

Morellato, L. P. C., B. Alberton, S. T. Alvarado, B. Borges, E. Buisson, M. G. G.

Camargo, et al. (2016). Linking plant phenology to conservation biology. Biological
Conservation, 195:60 – 72. ISSN 0006-3207. doi: 10.1016/j.biocon.2015.12.033.

Mosseri, R. and J. Catherine, editors (2013). L’énergie à découvert. CNRS Éditions,

Paris.

Mossio, M., M. Montévil, and G. Longo (2016). Theoretical principles for biology:
Organization. Progress in Biophysics and Molecular Biology, 122(1):24 – 35. ISSN
0079-6107. doi: 10.1016/j.pbiomolbio.2016.07.005.

Nicolis, G. and I. Prigogine (1977). Self-organization in non-equilibrium systems. Wiley,

New York.

Odling-Smee, F. J., K. N. Laland, and M. W. Feldman (2003). Niche construction: the

neglected process in evolution. Princeton University Press. ISBN 9780691044378.

28
Pocheville, A. (2010). What niche construction is (not).

Rafferty, N. E., P. J. CaraDonna, and J. L. Bronstein (2015). Phenological shifts and

the fate of mutualisms. Oikos, 124(1):14–21. doi: 10.1111/oik.01523.

Ripple, W. J., C. Wolf, T. M. Newsome, M. Galetti, M. Alamgir, E. Crist, et al.

(2017). World scientists warning to humanity: A second notice. BioScience,
67(12):1026–1028. doi: 10.1093/biosci/bix125.

Robbirt, K., D. Roberts, M. Hutchings, and A. Davy (2014). Potential disruption

of pollination in a sexually deceptive orchid by climatic change. Current Biology,
24(23):2845 – 2849. ISSN 0960-9822. doi: 10.1016/j.cub.2014.10.033.

Rogge, W. F., L. M. Hildemann, M. A. Mazurek, G. R. Cass, and B. R. T. Simoneit

(1993). Sources of fine organic aerosol. 3. road dust, tire debris, and organometallic
brake lining dust: roads as sources and sinks. Environmental Science & Technology,
27(9):1892–1904. doi: 10.1021/es00046a019.

Rosen, R. (1991). Life itself: a comprehensive inquiry into the nature, origin, and
fabrication of life. Columbia University Press, New York.

Rovelli, C. (2017). Is Time’s Arrow Perspectival?, page 285296. Cambridge University

Press. doi: 10.1017/9781316535783.015.

Schrödinger, E. (1944). What Is Life? Cambridge University Press, Londre.

Sethna, J. P. (2006). Statistical mechanics: Entropy, order parameters, and complexity.

Oxford University Press, New York. ISBN 0198566778.

Shannon, C. E. (1948). A mathematical theory of communication. The Bell System

Technical Journal, 27:379423.

Soto, A. M., G. Longo, D. Noble, N. Perret, M. Montévil, C. Sonnenschein, et al. (2016).

From the century of the genome to the century of the organism: New theoretical
approaches. Progress in Biophysics and Molecular Biology, Special issue, pages 1–82.

Soto, A. M., C. Sonnenschein, and P.-A. Miquel (2008). On physicalism and downward
causation in developmental and cancer biology. Acta Biotheoretica, 56(4):257–274.
doi: 10.1007/s10441-008-9052-y.

Stevenson, T. J., M. E. Visser, W. Arnold, P. Barrett, S. Biello, A. Dawson, et al. (2015).

Disrupted seasonal biology impacts health, food security and ecosystems. Proc Biol
Sci, 282(1817):20151453–20151453. ISSN 1471-2954. doi: 10.1098/rspb.2015.1453.

Stiegler, B. (2018). The neganthropocene. Open Humanites Press.

do Sul, J. A. I. and M. F. Costa (2014). The present and future of microplastic pollution
in the marine environment. Environmental Pollution, 185:352 – 364. ISSN 0269-7491.
doi: 10.1016/j.envpol.2013.10.036.

Templeton, A. R., R. J. Robertson, J. Brisson, and J. Strasburg (2001). Disrupting

evolutionary processes: The effect of habitat fragmentation on collared lizards in the
missouri ozarks. Proceedings of the National Academy of Sciences, 98(10):5426–5432.
ISSN 0027-8424. doi: 10.1073/pnas.091093098.

29
Turing, A. M. (1952). The chemical basis of morphogenesis. Philosophical Transactions
of the Royal Society of London. Series B, Biological Sciences, 237(641):37–72. doi: 10.
1098/rstb.1952.0012.

Varela, F., H. Maturana, and R. Uribe (1974). Autopoiesis: The organization of living
systems, its characterization and a model. Biosystems, 5(4):187 – 196. ISSN 0303-
2647. doi: 10.1016/0303-2647(74)90031-8.

Visser, M., S. Caro, K. Van Oers, S. Schaper, and B. Helm (2010). Phenology, sea-
sonal timing and circannual rhythms: towards a unified framework. Philosophi-
cal Transactions of the Royal Society B: Biological Sciences, 365(1555):3113–3127.
doi: 10.1098/rstb.2010.0111.

Williams, B. L., J. D. Brawn, and K. N. Paige (2003). Landscape scale genetic effects
of habitat fragmentation on a high gene flow species: Speyeria idalia (nymphalidae).
Molecular Ecology, 12(1):11–20. doi: 10.1046/j.1365-294X.2003.01700.x.

Wu, Y., M. Schuster, Z. Chen, Q. V. Le, M. Norouzi, W. Macherey, et al. (2016).

Google’s neural machine translation system: Bridging the gap between human and
machine translation. CoRR, abs/1609.08144.

Young, J. T. (1991). Is the entropy law relevant to the economics of natural resource
scarcity? Journal of Environmental Economics and Management, 21(2):169 – 179.
ISSN 0095-0696. doi: 10.1016/0095-0696(91)90040-P.

Zoeller, R. T., T. R. Brown, L. L. Doan, A. C. Gore, N. E. Skakkebaek, A. M. Soto, et al.

(2012). Endocrine-disrupting chemicals and public health protection: A statement
of principles from the endocrine society. Endocrinology, 153(9):4097–4110. doi: 10.
1210/en.2012-1422.

30