Zeroth law of thermodynamics for nonequilibrium steady states in contact

TL;DR

This paper investigates whether a zeroth law-like principle applies to nonequilibrium steady states when two such systems are in contact and exchange a conserved quantity, establishing conditions for the equalization of thermodynamic variables.

Contribution

It demonstrates that a zeroth law for nonequilibrium steady states holds under conditions of weak interaction and short-range correlations, extending thermodynamic principles beyond equilibrium.

Findings

Zeroth law applies to nonequilibrium steady states with certain conditions.

Weak interactions and short-range correlations are essential for the law to hold.

Validated the theory through various conserved-mass transport models.

Abstract

We ask what happens when two systems having a nonequilibrium steady state are kept in contact and allowed to exchange a quantity, say mass, which is conserved in the combined system. Will the systems eventually evolve to a new stationary state where certain intensive thermodynamic variable, like equilibrium chemical potential, equalizes following zeroth law of thermodynamics and, if so, under what conditions is it possible? We argue that the zeroth law would hold, provided both systems have short-ranged spatial correlations and they {\it interact weakly} to exchange mass with rates satisfying a balance condition - reminiscent of detailed balance in equilibrium. This proposition is proved for driven systems in general in the limit of small exchange rates (i.e., weak interaction) and is demonstrated} in various conserved-mass transport processes having nonzero spatial correlations.