Nonequilibrium microcanonical and canonical ensembles and their equivalence

TL;DR

This paper develops a unified theory of nonequilibrium microcanonical and canonical ensembles for Markov process paths, relating them to large deviation principles and establishing conditions for their equivalence.

Contribution

It generalizes previous ensemble theories for nonequilibrium systems, linking them to large deviations and providing a framework for constructing driven processes.

Findings

Conditions for ensemble equivalence are established.

A method to construct driven processes generating these ensembles.

Illustration with a nonequilibrium diffusion model.

Abstract

Generalizations of the microcanonical and canonical ensembles for paths of Markov processes have been proposed recently to describe the statistical properties of nonequilibrium systems driven in steady states. Here we propose a theory of these ensembles that unifies and generalizes earlier results, and show how it is fundamentally related to the large deviation properties of nonequilibrium systems. Using this theory, we provide conditions for the equivalence of nonequilibrium ensembles, generalizing those found for equilibrium systems, construct driven physical processes that generate these ensembles, and re-derive in a simple way known and new product rules for their transition rates. A nonequilibrium diffusion model is used to illustrate these results.