Current fluctuations in periodically driven systems

TL;DR

This paper develops a formalism to evaluate large current fluctuations in small periodically driven systems, revealing that the fluctuations are characterized by a maximal Floquet exponent and comparing deterministic and stochastic protocols.

Contribution

The authors introduce a theoretical framework linking current fluctuation large deviations to Floquet theory in periodically driven Markov systems, including stochastic and deterministic protocols.

Findings

Large deviations are characterized by a maximal Floquet exponent.

Stochastic protocols with infinite jumps are equivalent to deterministic protocols for large deviations.

Illustrations include models of heat engines, molecular pumps, and biased random walks.

Abstract

Small nonequelibrium systems driven by an external periodic protocol can be described by Markov processes with time-periodic transition rates. In general, current fluctuations in such small systems are large and may play a crucial role. We develop a theoretical formalism to evaluate the rate of such large deviations in periodically driven systems. We show that the scaled cumulant generating function that characterizes current fluctuations is given by a maximal Floquet exponent. Comparing deterministic protocols with stochastic protocols, we show that, with respect to large deviations, systems driven by a stochastic protocol with an infinitely large number of jumps are equivalent to systems driven by deterministic protocols. Our results are illustrated with three case studies: a two-state model for a heat engine, a three-state model for a molecular pump, and a biased random walk with a time-periodic affinity.