Islands of equilibrium in a dynamical world

TL;DR

This paper demonstrates how equilibrium-like regions can spontaneously form within inherently non-equilibrium systems, depending on system parameters and network connectivity, revealing complex localized behaviors.

Contribution

It provides a detailed analysis of exemplar models showing the emergence and disappearance of equilibrium domains in non-equilibrium systems based on network structure and parameters.

Findings

Equilibrium domains can emerge abruptly or gradually.

Such domains can disappear and blend into the non-equilibrium background.

Models on various network connectivities effectively represent real systems.

Abstract

Many natural, technological and social systems are inherently not in equilibrium. We show, by detailed analysis of exemplar models, the emergence of equilibrium-like behavior in localized or nonlocalized domains within non-equilibrium systems as conjectured in some real systems. Equilibrium domains are shown to emerge either abruptly or gradually depending on the system parameters and disappear, becoming indistinguishable from the remainder of the system for other parameter values. The models studied, defined on densely and sparsely connected networks, provide a useful representation of many real systems.