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  • Open Access

Inferring Entropy Production in Many-Body Systems Using Nonequilibrium Maximum Entropy

Miguel Aguilera1,2,*,†, Sosuke Ito3,4, and Artemy Kolchinsky5,3,*,‡

  • *These authors contributed equally to this work.
  • †Contact author: maguilera@bcamath.org
  • ‡Contact author: artemyk@gmail.com
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Phys. Rev. Lett. 136, 077101 – Published 18 February, 2026

DOI: https://doi.org/10.1103/xgkj-dxzh

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.

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Phys. Rev. Lett. 136, 077101– Published 18 February, 2026
  • Received 6 June 2025
  • Revised 10 September 2025
  • Accepted 18 December 2025
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