Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jun;91(6):062136. doi: 10.1103/PhysRevE.91.062136. Epub 2015 Jun 25.

Zeroth law and nonequilibrium thermodynamics for steady states in contact.

Physical review. E, Statistical, nonlinear, and soft matter physics

Sayani Chatterjee, Punyabrata Pradhan, P K Mohanty

PMID: 26172690 DOI: 10.1103/PhysRevE.91.062136

Abstract

We ask what happens when two nonequilibrium systems in 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 a certain intensive thermodynamic variable, like equilibrium chemical potential, equalizes following the zeroth law of thermodynamics and, if so, under what conditions is it possible? We argue that an equilibriumlike thermodynamic structure can be extended to nonequilibrium steady states having short-ranged spatial correlations, provided that the systems interact weakly to exchange mass with rates satisfying a balance condition-reminiscent of a detailed balance condition in equilibrium. The short-ranged correlations would lead to subsystem factorization on a coarse-grained level and the balance condition ensures both equalization of an intensive thermodynamic variable as well as ensemble equivalence, which are crucial for construction of a well-defined nonequilibrium thermodynamics. This proposition is proved and demonstrated in various conserved-mass transport processes having nonzero spatial correlations.

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• Journal Article