Inconsistencies in steady state thermodynamics

Abstract

We address the issue of extending thermodynamics to nonequilibrium steady states. Using driven stochastic lattice gases, we ask whether consistent definitions of an effective chemical potential mu, and an effective temperature T_e, are possible. mu and T_e are determined via coexistence, i.e., zero flux of particles and energy between the driven system and a reservoir. In the lattice gas with nearest-neighbor exclusion, temperature is not relevant, and we find that the effective chemical potential, a function of density and drive strength, satisfies the zeroth law, and correctly predicts the densities of coexisting systems. In the Katz-Lebowitz-Spohn driven lattice gas both mu and T_e need to be defined. We show analytically that in this case the zeroth law is violated for Metropolis exchange rates, and determine the size of the violations numerically. The zeroth law appears to be violated for generic exchange rates. Remarkably, the system-reservoir coupling proposed by Sasa and Tasaki [J. Stat. Phys. 125, 125 (2006)], is free of inconsistencies, and the zeroth law holds. This is because the rate depends only on the state of the donor system, and is independent of that of the acceptor.

12 pages, 1 figure Extended version with important amendments regarding absence of inconsistencies using Sasa-Tasaki exchange rates

References in corpus (3)

• Monte Carlo simulations of 2d hard core lattice gases
• Intensive thermodynamic parameters in nonequilibrium systems
• Absorbing-state phase transitions: exact solutions of small systems

Cited by in corpus (9)

• Phase coexistence of active Brownian particles
• Exact equalities and thermodynamic relations for nonequilibrium steady states
• Lack of an equation of state for the nonequilibrium chemical potential of gases of active particles in contact
• Zeroth law of thermodynamics for nonequilibrium steady states in contact
• Large deviations and chemical potential in bulk-driven systems in contact
• Driven Widom-Rowlinson lattice gas
• Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviations approach
• Nonequilibrium grand-canonical ensemble built from a physical particle reservoir
• Non-additive large deviations function for the particle densities of driven systems in contact