Identifying nonequilibrium degrees of freedom in high-dimensional stochastic systems

2025/08/11 by Ji, Catherine, Raj, Ravin, Eysenbach, Benjamin +1
#Biological Physics (physics.bio-ph) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2508.08247

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.

Citations

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Related

• Model-free learning of probability flows: Elucidating the nonequilibrium dynamics of flocking
• Identifiable learning of dissipative dynamics
• Inferring entropy production in many-body systems using nonequilibrium maximum entropy
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