Level 2.5 large deviations for continuous time Markov chains with time periodic rates

TL;DR

This paper establishes large deviation principles for empirical measures, flows, and currents in continuous-time Markov chains with periodic rates, deriving duality relations and discussing applications.

Contribution

It introduces joint large deviation principles for empirical measures, flows, and currents in time-periodic Markov chains, including entropy production flows.

Findings

Large deviation principles for empirical measure and flow

Large deviation principles for empirical measure and current

Gallavotti-Cohen duality relations derived

Abstract

We consider an irreducible continuous time Markov chain on a finite state space and with time periodic jump rates and prove the joint large deviation principle for the empirical measure and flow and the joint large deviation principle for the empirical measure and current. By contraction we get the large deviation principle of three types of entropy production flow. We derive some Gallavotti-Cohen duality relations and discuss some applications.