Irreversibility in non-reciprocal chaotic systems

How is the irreversibility of a high-dimensional chaotic system related to its dynamical behavior? In this paper, we address this question by developing a stochastic-thermodynamics treatment of complex networks that exhibit chaos. Specifically, we establish an exact relation between the averaged entropy production rate-a measure of irreversibility-and the autocorrelation function for an infinite system of neurons coupled via random non-reciprocal interactions. We show how, under given noise strength, the entropy production rate can signal the onset of a transition occurring as the coupling heterogeneity increases beyond a critical value via a change in its functional form upon crossing this point. Furthermore, this transition happens at a fixed, noise-independent entropy production rate, elucidating how robust energetic cost is possibly responsible for optimal information processing at criticality.