Inferring entropy production in many-body systems using nonequilibrium MaxEnt

2025-05-15

AI Summary

Estimating trajectory-level entropy production (EP) in high-dimensional stochastic systems—such as disordered 1000-spin nonequilibrium models and large-scale neural spike trains—is hindered by prohibitive computational complexity and insufficient statistical sampling, rendering conventional methods inapplicable. To address this, we propose a novel inference framework grounded in the nonequilibrium maximum entropy principle and convex duality. Our approach requires only low-order spatiotemporal correlation functions as input observables, avoiding full reconstruction of the high-dimensional state distribution, assumptions of discrete states, or modular system structure. Theoretically, it enables hierarchical decomposition of EP and yields a functional dual interpretation of the thermodynamic uncertainty relation. Algorithmically, it leverages statistical inference from trajectory observables and dual characterization of the EP functional to achieve superior scalability. We validate the method on a 1000-spin disordered model and real neural electrophysiological data, overcoming simultaneous bottlenecks in both dimensionality and data scale.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Information Theory
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

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 correlation functions). It does not require reconstruction of high-dimensional probability distributions or rate matrices, nor any special assumptions such as discrete states or multipartite dynamics. It may be used to compute a hierarchical decomposition of EP, reflecting contributions from different kinds of interactions, 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.

Problem

• Estimating entropy production in high-dimensional stochastic systems
• Overcoming computational limits in many-body and non-Markovian systems
• Inferring EP without reconstructing probability distributions or rate matrices

Innovation

• Uses nonequilibrium MaxEnt for entropy inference
• Leverages convex duality with trajectory observables
• Computes hierarchical EP decomposition intuitively