The explicit form of the rate function for semi-Markov processes and its contractions

TL;DR

This paper derives an explicit rate function for semi-Markov processes using the random time change trick, demonstrating the fluctuation theorem and extending the Level 2.5 rate function from Markov to semi-Markov processes.

Contribution

It provides the explicit form of the rate function for semi-Markov processes and extends the Level 2.5 rate function to this broader class.

Findings

The fluctuation theorem (Gallavotti-Cohen Symmetry) holds for semi-Markov processes.

The rate function is explicitly derived using the random time change trick.

The rate function extends the Level 2.5 rate function from Markov to semi-Markov processes.

Abstract

We derive the explicit form of the rate function for semi-Markov processes. Here, the "random time change trick" plays an essential role. Also, by exploiting the contraction principle of the large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen Symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the Level 2.5 rate function for Markov processes to semi-Markov cases.