Comment on `Detailed balance has a counterpart in non-equilibrium steady states'

TL;DR

This paper discusses the derivation of transition rates in non-equilibrium steady states, demonstrating the consistency between continuous and discretized models, and clarifying the characterization of reservoirs by mean energy and flux.

Contribution

It shows the equivalence of transition rate prescriptions in continuous and discrete time models of driven steady states, confirming theoretical consistency.

Findings

Demonstrates the equivalence of continuous and discretized time models.

Confirms the reservoir is characterized by mean energy and flux.

Provides a consistent framework for modeling non-equilibrium steady states.

Abstract

Transition rates in continuously driven steady states were derived in [Evans R M L, 2005 J. Phys. A: Math. Gen. 38, 293] by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the system be used to describe it. In addition to the mean energy at equilibrium, and unlike them, these driven states have a finite throughput of flux. This implies that the (nonequilibrium) reservoir, to which the system is weakly coupled, is fully characterised by its mean energy and mean flux. While we expect the resulting prescription for the rates in continuous and discretised time versions of models of real systems to be equivalent, it is not trivial to see this from the expression for the rates derived previously. We demonstrate this equivalence for a model of activated processes solved previously for continuous time, thus demonstrating consistency of theory.