Large deviation principles and fluctuation theorems for currents in semi-Markov processes

TL;DR

This paper establishes large deviation principles and fluctuation theorems for currents in semi-Markov processes with direction-time independence, extending the theoretical understanding of their probabilistic behavior.

Contribution

It derives new large deviation principles and fluctuation theorems specifically for empirical currents in semi-Markov processes, building on recent joint LDP results.

Findings

Large deviation principles for empirical currents in semi-Markov processes.

Fluctuation theorems for currents along cycles.

Extension of probabilistic frameworks to semi-Markov processes.

Abstract

In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the empirical currents along cycles. Our derivation is based on the joint LDP for the empirical measure and flow recently proved in \cite{MZ}.