Nonequilibrium entropy from density estimation

TL;DR

This paper introduces a machine learning-based method to estimate nonequilibrium entropy from system configurations by mapping them to images and using density estimation, enabling analysis of complex stochastic dynamics.

Contribution

It presents a novel approach to estimate nonequilibrium entropy using image-based density estimation techniques applied to simulated and experimental data.

Findings

Successfully estimated entropy in a driven kinetic Ising model.

Identified entropic limit cycles near a dynamical phase transition.

Demonstrated the method's applicability to complex stochastic systems.

Abstract

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated configurations. However, modern machine learning algorithms can estimate the probability density characterizing an ensemble of images, given nothing more than sample images assumed to be drawn from this distribution. We show that by mapping system configurations to images, such approaches can be adapted to the efficient estimation of the density, and therefore the entropy, from simulated or experimental data. We then use this idea to obtain entropic limit cycles in a kinetic Ising model driven by an oscillating magnetic field. Despite being a global probe, we demonstrate that this allows us to identify and characterize stochastic dynamics at parameters near the dynamical phase transition.