Similarities and Differences Between Nonequilibrium Steady States and Time-Periodic Driving in Diffusive Systems
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.
Keywords
Cite
@article{arxiv.1807.04104,
title = {Similarities and Differences Between Nonequilibrium Steady States and Time-Periodic Driving in Diffusive Systems},
author = {Daniel M. Busiello and Christopher Jarzynski and Oren Raz},
journal= {arXiv preprint arXiv:1807.04104},
year = {2018}
}