Nonequilibrium physics aspects of probabilistic cellular automata

TL;DR

This paper explores nonequilibrium phenomena in probabilistic cellular automata, linking classical concepts like detailed balance, entropy production, and fluctuation symmetry to these models, and deriving related formulas.

Contribution

It introduces a framework embedding nonequilibrium concepts into PCA, including Kubo formulas, McLennan distribution, and fluctuation symmetry, extending understanding of PCA beyond equilibrium.

Findings

Kubo formula for linear response in time-symmetric PCA

Characterization of McLennan distribution near detailed balance

Fluctuation symmetry for entropy flux in broken time-symmetry stationary states

Abstract

Probabilistic cellular automata (PCA) are used to model a variety of discrete spatially extended systems undergoing parallel-updating. We propose an embedding of a number of classical nonequilibrium concepts in the PCA-world. We start from time-symmetric PCA, satisfying detailed balance, and we give their Kubo formula for linear response. Close-to-detailed balance we investigate the form of the McLennan distribution and the minimum entropy production principle. More generally, when time-symmetry is broken in the stationary process, there is a fluctuation symmetry for a corresponding entropy flux. For linear response around nonequilibria we also give the appropriate formula which is now not only entropic in nature.