Large deviations and chemical potential in bulk-driven systems in contact

TL;DR

This paper investigates the conditions under which nonequilibrium chemical potentials can be defined for bulk-driven systems in contact, revealing that they generally differ from isolated system potentials and do not follow an equation of state, but certain classes obey thermodynamic laws.

Contribution

It establishes that chemical potentials can be defined in weak contact limits when exchange dynamics factorizes and satisfies macroscopic detailed balance, extending thermodynamic concepts to nonequilibrium systems.

Findings

Chemical potentials can be defined under specific conditions in nonequilibrium systems.

These potentials generally differ from those of isolated systems and lack an equation of state.

Some classes of systems still obey the zeroth law of thermodynamics.

Abstract

We study whether the stationary state of two bulk-driven systems slowly exchanging particles can be described by the equality of suitably defined nonequilibrium chemical potentials. Our main result is that in a weak contact limit, chemical potentials can be defined when the dynamics of particle exchange takes a factorized form with respect to the two systems, and satisfies a macroscopic detailed balance property at large deviation level. The chemical potentials of systems in contact generically differ from the nonequilibrium chemical potentials of isolated systems, and do not satisfy an equation of state. Yet, classes of systems satisfying the zeroth law of thermodynamics can be defined in a natural way. These results are illustrated on a driven lattice particle model and on an active particle model. The case when a chemical potential cannot be defined also has interesting consequences, like a non-standard form of the grand-canonical ensemble.