Far-from-equilibrium complex landscapes

TL;DR

This paper generalizes the concept of complex landscapes to far-from-equilibrium systems, demonstrating how collective states with spontaneous oscillations can be characterized using entropy-based observables.

Contribution

It introduces a framework for analyzing complex landscapes in nonequilibrium systems, including a method to identify oscillations via entropy production and a way to quantify states with configurational entropy.

Findings

Identification of spontaneous oscillations in nonequilibrium landscapes

Use of entropy production density to detect hidden collective states

Quantification of landscape complexity through configurational entropy

Abstract

Systems with a complex dynamics like glasses or models of biological evolution are often pictured in terms of complex landscapes, with a large number of possible collective states. We show on the example of a stochastic spin model with non-reciprocal and heterogeneous interactions how the complex landscape notion can be generalized far from equilibrium, where collective states may exhibit spontaneous oscillations, often hidden by the presence of disorder. We identify relevant observables, like the density of entropy production, to unveil the presence of oscillations, and we characterize the complex landscape of our model in terms of a configurational entropy, that counts the number of nonequilibrium collective states with a given entropy production density.