Identifying nonequilibrium degrees of freedom in high-dimensional stochastic systems

TL;DR

This paper presents a novel, model-free method called LENS that uses classification of forward and reversed trajectories to identify irreversible degrees of freedom and estimate entropy production in high-dimensional nonequilibrium systems.

Contribution

The paper introduces LENS, a scalable, learning-based approach that uncovers low-dimensional irreversible flows and estimates entropy production directly from high-dimensional data.

Findings

LENS accurately identifies irreversible dynamics in high-dimensional systems.

LENS provides reliable estimates of entropy production rates.

The method is scalable and applicable to complex stochastic systems.

Abstract

Any coarse-grained description of a nonequilibrium system should faithfully represent its latent irreversible degrees of freedom. However, standard dimensionality reduction methods typically prioritize accurate reconstruction over physical relevance. Here, we introduce a model-free approach to identify irreversible degrees of freedom in stochastic systems that are in a nonequilibrium steady state. Our method leverages the insight that a black-box classifier, trained to differentiate between forward and time-reversed trajectories, implicitly estimates the local entropy production rate. By parameterizing this classifier as a quadratic form of learned state representations, we obtain nonlinear embeddings of high-dimensional state-space dynamics, which we term Latent Embeddings of Nonequilibrium Systems (LENS). LENS effectively identifies low-dimensional irreversible flows and provides a scalable, learning-based strategy for estimating entropy production rates directly from high-dimensional time series data.