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

arXiv: https://arxiv.org/abs/2505.10444 · HTML: https://mlsanity.com/paper/2505.10444/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 79 references that are in the map.
- First posted on arXiv 15 May 2025.

## Builds on (most cited first, 11 of 11)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Inverse statistical problems: from the inverse Ising problem to data science](https://mlsanity.com/paper/1702.01522/) (2017)
- [Deep learning probability flows and entropy production rates in active matter](https://mlsanity.com/paper/2309.12991/) (2023)
- [Learning entropy production via neural networks](https://mlsanity.com/paper/2003.04166/) (2020)
- [A unifying framework for mean-field theories of asymmetric kinetic Ising systems](https://mlsanity.com/paper/2002.04309/) (2020)
- [Broken detailed balance and entropy production in the human brain](https://mlsanity.com/paper/2005.02526/) (2020)
- [Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics](https://mlsanity.com/paper/2312.03489/) (2023)
- [Nonequilibrium physics of brain dynamics](https://mlsanity.com/paper/2504.12188/) (2025)
- [Decomposing the local arrow of time in interacting systems](https://mlsanity.com/paper/2112.14721/) (2021)
- [Emergence of local irreversibility in complex interacting systems](https://mlsanity.com/paper/2203.01916/) (2022)
- [State-space kinetic Ising model reveals task-dependent entropy flow in sparsely active nonequilibrium neuronal dynamics](https://mlsanity.com/paper/2502.15440/) (2025)

## Built on by (most cited first, 1 of 1)

- [Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks](https://mlsanity.com/paper/2602.14885/) (2026)

## Abstract (arXiv)

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.