Approximate thermodynamic structure for driven lattice gases in contact

TL;DR

This paper investigates driven lattice gases in contact, showing that an approximate chemical potential can describe their steady states, but contact dynamics cause deviations, leading to a potential violation of the zeroth law of thermodynamics.

Contribution

It introduces the concept of excess chemical potential to account for deviations caused by contact dynamics in nonequilibrium driven lattice gases.

Findings

Approximate chemical potential can describe steady states in driven lattice gases.

Deviations from thermodynamic laws are due to contact dynamics.

Excess chemical potential explains contact-dependent deviations.

Abstract

For a class of nonequilibrium systems, called driven lattice gases, we study what happens when two systems are kept in contact and allowed to exchange particles with the total number of particles conserved. Both for attractive and repulsive nearest-neighbor interactions among particles and for a wide range of parameter values, we find that, to a good approximation, one could define an intensive thermodynamic variable, like equilibrium chemical potential, which determines the final steady state for two initially separated driven lattice gases brought into contact. However, due to nontrivial contact dynamics, there are also observable deviations from this simple thermodynamic law. To illustrate the role of the contact dynamics, we study a variant of the zero range process and discuss how the deviations could be explained by a modified large deviation principle. We identify an additional contribution to the large deviation function, which we call the excess chemical potential, for the variant of the zero range process as well as the driven lattice gases. The excess chemical potential depends on the specifics of the contact dynamics and is in general a-priori unknown. A contact dependence implies that even though an intensive variable may equalize, the zeroth law could still be violated.