Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviations approach

TL;DR

This paper develops a large-deviations framework to define and analyze chemical potentials in nonequilibrium steady-state lattice gas models in contact, revealing conditions for additivity and the influence of contact dynamics.

Contribution

It introduces a general approach to define nonequilibrium chemical potentials in contact systems, highlighting the role of macroscopic detailed balance and contact dynamics.

Findings

Additivity of large-deviations function under certain conditions

Chemical potentials depend on contact dynamics and do not obey an equation of state

Application to exactly solvable and numerical lattice gas models

Abstract

We introduce a general framework to describe the stationary state of two driven systems exchanging particles or mass through a contact, in a slow exchange limit. The definition of chemical potentials for the systems in contact requires that the large-deviations function describing the repartition of mass between the two systems is additive, in the sense of being a sum of contributions from each system. We show that this additivity property is satisfied on condition that a macroscopic detailed balance condition holds at contact, and that the coarse-grained contact dynamics satisfies a factorization property. However, the nonequilibrium chemical potentials of the systems in contact keep track of the contact dynamics, and thus do not obey an equation of state. These nonequilibrium chemical potentials can be related either to the equilibrium chemical potential, or to the nonequilibrium chemical potential of the isolated systems. Results are applied both to an exactly solvable driven lattice gas model, and to the Katz-Lebowitz-Spohn model using a numerical procedure to evaluate the chemical potential.