This is a proof-of-concept implementation of a 1D nonequilibrium molecular dynamics simulation which computes gauge correlation functions via automatic and finite initial-state time differentiation as described in:

Dynamical gauge invariance of statistical mechanics
Johanna Müller, Florian Sammüller, and Matthias Schmidt; arXiv:2504.17599.

A recent version of Julia needs to be installed on your system. Launch the Julia interpreter within this directory and type ] to enter the package manager. Activate the environment and install the required packages as follows:

activate .
instantiate

Type backspace to exit the package manager.

Fetch pregenerated data (~2GB) and reproduce the plots from the manuscript:

using Downloads, Tar
Downloads.download("https://www.staff.uni-bayreuth.de/~bt306964/dynamical-gauge/data.tar", "data.tar")
Tar.extract("data.tar", "data")
include("plot_paper.jl")

Check and adapt the settings of the run in main.jl and perform a custom nonequilibrium simulation:

include("main.jl")

Inspect the sampled gauge correlation functions of the previous run:

include("plot_all_histograms.jl")