Zeroth law and nonequilibrium thermodynamics for steady states in contact

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.

Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles

“…Recently, additivity has been used in nonequilibrium mass-transport processes for calculating mass distributions and characterizing macroscopic properties in terms of equilibriumlike thermodynamic potentials [8,9]. Below, we discuss how additivity can be used to calculate subsystem particle-number distribution.…”

“…At this scenario, additivity, which originates from the simple physical consideration of statistical independence on the coarse-grained level of large subsystems, could help us to bypass the difficulty. As demonstrated recently in [8,9], to characterize fluctuation properties on a coarsegrained level, one may not actually be required to obtain the steady-state weights of all microscopic configurations. In fact, obtaining coarse-grained probability weights on a large scale (much larger than the microscopic correlation length scale) would suffice to characterize the macroscopic properties of the system, provided that additivity as in Eq.…”

“…A simple characterization of the steady-state systems in general would be certainly desirable and, to this end, various attempts have been made in the past [3,4]. Recently, a formulation based on equilibriumlike additivity property provides a framework [5][6][7], which helps one to describe a broad class of nonequilibrium steady states through fluctuations of a conserved quantity, e.g., mass or particle-number [8][9][10]. Here, we address the question whether an additivity property can be used to obtain large deviation probability for the particle-number or the density fluctuations, the central object in a statistical mechanics theory, in systems of self-propelled particles.…”

Phase coexistence far from equilibrium

“…A central issue in nonequilibrium physics is whether thermodynamics can be extended to systems far from equilibrium, in particular, to steady states [1][2][3][4][5][6][7][8][9][10][11][12]. A key thermodynamic concept is phase coexistence; indeed, one of the principal applications of equilibrium thermodynamics is the prediction of phase coexistence based upon knowledge of the isolated phases.…”

“…Despite the inconsistencies noted in [18], Pradhan and Seifert [9] were able to construct a mean-field theory of phase coexistence in the driven lattice gas that compares well with simulation. Chatterjee and coworkers [10,11] have argued that ITPs can be defined consistently for interacting systems in NESS provided spatial correlations are short-ranged, and that the systems interact weakly.…”