# Decomposing the local arrow of time in interacting systems

arXiv: https://arxiv.org/abs/2112.14721 · HTML: https://mlsanity.com/paper/2112.14721/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2021.

## Built on by (most cited first, 3 of 3)

- [Generative learning for nonlinear dynamics](https://mlsanity.com/paper/2311.04128/) (2023)
- [Inferring entropy production in many-body systems using nonequilibrium maximum entropy](https://mlsanity.com/paper/2505.10444/) (2025)
- [Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks](https://mlsanity.com/paper/2602.14885/) (2026)

## Abstract (arXiv)

We show that the evidence for a local arrow of time, which is equivalent to the entropy production in thermodynamic systems, can be decomposed. In a system with many degrees of freedom, there is a term that arises from the irreversible dynamics of the individual variables, and then a series of non--negative terms contributed by correlations among pairs, triplets, and higher--order combinations of variables. We illustrate this decomposition on simple models of noisy logical computations, and then apply it to the analysis of patterns of neural activity in the retina as it responds to complex dynamic visual scenes. We find that neural activity breaks detailed balance even when the visual inputs do not, and that this irreversibility arises primarily from interactions between pairs of neurons.