On the definition of equilibrium and non-equilibrium states in dynamical systems

TL;DR

This paper introduces a new definition for equilibrium and non-equilibrium states in dynamical systems based on time averages and demonstrates the existence of a non-equilibrium non-stationary state through numerical analysis.

Contribution

It proposes a novel definition of equilibrium states in dynamical systems and provides numerical evidence of non-equilibrium non-stationary states in a coupled map lattice.

Findings

Existence of non-equilibrium non-stationary states in coupled Bernoulli map lattice

New definition of equilibrium based on time averages

Numerical validation of theoretical concepts

Abstract

We propose a definition of equilibrium and non-equilibrium states in dynamical systems on the basis of the time average. We show numerically that there exists a non-equilibrium non-stationary state in the coupled modified Bernoulli map lattice.