Periodically driven jump processes conditioned on large deviations

TL;DR

This paper investigates the fluctuations of Markov jump processes with periodic generators, using large deviation theory and transformations to characterize the asymptotic behavior of time-periodic observables.

Contribution

It introduces a method to identify the driven process that minimizes the large deviation function for occupation and jumps in periodically driven systems.

Findings

Characterizes the driven process via large deviation principles.

Shows the driven process minimizes the large deviation function.

Provides a framework for analyzing fluctuations in periodically driven Markov systems.

Abstract

We study the fluctuations of systems modeled by Markov jump processes with periodic generators. We focus on observables defined through time-periodic functions of the system's states or transitions. Using large deviation theory, canonical biasing and generalized Doob transform, we characterize the asymptotic fluctuations of such observables after a large number of periods by obtaining the Markov process that produces them. We show that this process, called driven process, is the minimum under constraint of the large deviation function for occupation and jumps.