Inferring entropy production in many-body systems using nonequilibrium maximum entropy

TL;DR

This paper introduces a novel method to infer entropy production in complex many-body and non-Markovian systems using a nonequilibrium maximum entropy approach, avoiding high-dimensional probability reconstructions.

Contribution

It develops a trajectory-based inference technique for entropy production that leverages maximum entropy principles and convex duality, applicable to high-dimensional and memory-dependent systems.

Findings

Successfully applied to a 1000-spin disordered spin model

Effective in analyzing large neural spike-train datasets

Provides hierarchical decomposition of entropy production

Abstract

We propose a method for inferring entropy production (EP) in high-dimensional stochastic systems, including many-body systems and non-Markovian systems with long memory. Standard techniques for estimating EP become intractable in such systems due to computational and statistical limitations. We infer trajectory-level EP and lower bounds on average EP by exploiting a nonequilibrium analogue of the Maximum Entropy principle, along with convex duality. Our approach uses only samples of trajectory observables, such as spatiotemporal correlations. It does not require reconstruction of high-dimensional probability distributions or rate matrices, nor impose any special assumptions such as discrete states or multipartite dynamics. In addition, it may be used to compute a hierarchical decomposition of EP, reflecting contributions from different interaction orders, and it has an intuitive physical interpretation as a "thermodynamic uncertainty relation." We demonstrate its numerical performance on a disordered nonequilibrium spin model with 1000 spins and a large neural spike-train dataset.