Similarities and Differences Between Nonequilibrium Steady States and Time-Periodic Driving in Diffusive Systems

TL;DR

This paper compares nonequilibrium steady states and time-periodic driving in diffusive systems, showing that periodic driving generally produces higher entropy but can be tuned to approach steady state entropy levels.

Contribution

It provides a detailed comparison of entropy production in steady and periodically driven diffusive systems, including methods to construct states supporting the same currents and distributions.

Findings

Periodic driving yields higher entropy production than steady states.

The entropy difference between the two can be made arbitrarily small.

Constructive methods for both steady and periodic states are provided.

Abstract

A system that violates detailed balance evolves asymptotically into a nonequilibrium steady state with non-vanishing currents. Analogously, when detailed balance holds at any instant of time but the system is driven through time-periodic variations of external parameters, it evolves toward a time-periodic state, which can also support non-vanishing currents. In both cases the maintenance of currents throughout the system incurs a cost in terms of entropy production. Here we compare these two scenarios for one dimensional diffusive systems with periodic boundary condition, a framework commonly used to model biological and artificial molecular machines. We first show that the entropy production rate in a periodically driven system is necessarily greater than that in a stationary system without detailed balance, when both are described by the same (time-averaged) current and probability distribution. Next, we show how to construct both a non-equilibrium steady state and a periodic driving that support a given time averaged probability distribution and current. Lastly, we show that although the entropy production rate of a periodically driven system is higher than that of an equivalent steady state, the difference between the two entropy production rates can be tuned to be arbitrarily small.