Mimicking Nonequilibrium Steady States with Stochastic Pumps

TL;DR

This paper demonstrates a theoretical equivalence between nonequilibrium steady states and stochastic pumps, showing how one can mimic the other in discrete systems by matching currents and entropy production.

Contribution

It establishes a general mapping between NESS and stochastic pumps, revealing their fundamental equivalence in discrete-state systems.

Findings

Stochastic pumps can replicate NESS behavior in terms of currents and entropy production.

A systematic method to construct a stochastic pump from a given NESS.

The equivalence holds in both directions, from NESS to SP and vice versa.

Abstract

We establish a correspondence between two very general paradigms for systems that persist away from thermal equilibrium. In the first paradigm, a nonequilibrium steady state (NESS) is maintained by applying fixed thermodynamic forces that break detailed balance. In the second paradigm, known as a stochastic pump (SP), a time-periodic state is maintained by the periodic variation of a system's external parameters. In both cases, currents are generated and entropy is produced. Restricting ourselves to discrete-state systems, we establish a mapping between these scenarios. Given a NESS characterized by a particular set of stationary probabilities, currents and entropy production rates, we show how to construct a SP with exactly the same (time-averaged) values. The mapping works in the opposite direction as well. These results establish an equivalence between the two paradigms, by showing that stochastic pumps are able to mimic the behavior of nonequilibrium steady states, and vice-versa.