Decomposing the local arrow of time in interacting systems

TL;DR

This paper introduces a decomposition of the local arrow of time in interacting systems, revealing how irreversibility arises from individual dynamics and correlations, with applications to neural activity analysis.

Contribution

It presents a novel decomposition method for local entropy production, applied to neural systems, highlighting the role of pairwise interactions in irreversibility.

Findings

Neural activity exhibits irreversibility even without external stimuli.

Irreversibility mainly stems from pairwise interactions among neurons.

The decomposition clarifies sources of entropy production in complex systems.

Abstract

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.