Dynamical fluctuations for semi-Markov processes

TL;DR

This paper develops a large deviation theory for nonequilibrium semi-Markov processes, revealing how non-Markovian features influence occupation and current fluctuations with explicit solutions for specific models.

Contribution

It introduces an Onsager-Machlup-type framework for semi-Markov processes and derives exact asymptotics for occupation and current probabilities, highlighting nonlocal fluctuation effects.

Findings

Derived large deviation structures for semi-Markov processes

Showed influence of non-exponential waiting times on fluctuations

Provided explicit solutions for driven ring models

Abstract

We develop an Onsager-Machlup-type theory for nonequilibrium semi-Markov processes. Our main result is an exact large time asymptotics for the joint probability of the occupation times and the currents in the system, establishing some generic large deviation structures. We discuss in detail how the nonequilibrium driving and the non-exponential waiting time distribution influence the occupation-current statistics. The violation of the Markov condition is reflected in the emergence of a new type of nonlocality in the fluctuations. Explicit solutions are obtained for some examples of driven random walks on the ring.