Irreversibility in Non-reciprocal Chaotic Systems

TL;DR

This paper investigates how heterogeneity in non-reciprocal interactions influences irreversibility in high-dimensional chaotic systems, using a stochastic neural network model and dynamical mean field theory to derive exact and approximate entropy production rates.

Contribution

It provides an exact analytical expression for irreversibility in a high-dimensional chaotic system with non-reciprocal interactions, revealing how it changes at the chaos transition.

Findings

Entropy production rate becomes constant at chaos onset

Functional form of irreversibility changes across the transition

Closed-form approximations describe behavior below and above critical heterogeneity

Abstract

How is the irreversibility of a high-dimensional chaotic system controlled by the heterogeneity in the non-reciprocal interactions among its elements? In this paper, we address this question using a stochastic model of random recurrent neural networks that undergoes a transition from quiescence to chaos at a critical heterogeneity. In the thermodynamic limit, using dynamical mean field theory, we obtain an exact expression for the averaged entropy production rate - a measure of irreversibility - for any heterogeneity level J. We show how this quantity becomes a constant at the onset of chaos while changing its functional form upon crossing this point. The latter can be elucidated by closed-form approximations valid for below and slightly above the critical point and for large J.