Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states

TL;DR

This paper introduces a classification of non-equilibrium steady states based on probability currents, providing a graph-theoretical framework to analyze their invariance and implications for entropy production.

Contribution

It presents a novel classification of NESS centered on probability currents and details how transition rates can be transformed without altering the steady state.

Findings

Probability currents are key to classifying NESS.

Transformations of transition rates can leave NESS invariant.

Implications for entropy production are discussed.

Abstract

One of the key features of non-equilibrium steady states (NESS) is the presence of nontrivial probability currents. We propose a general classification of NESS in which these currents play a central distinguishing role. As a corollary, we specify the transformations of the dynamic transition rates which leave a given NESS invariant. The formalism is most transparent within a continuous time master equation framework since it allows for a general graph-theoretical representation of the NESS. We discuss the consequences of these transformations for entropy production, present several simple examples, and explore some generalizations, to discrete time and continuous variables.