A formal view on 2.5 large deviations and fluctuation relations

TL;DR

This paper derives the rate function for level 2.5 large deviations in jump and diffusion processes using tilting and spectral methods, and explores their connection to fluctuation relations.

Contribution

It provides a rigorous derivation of the level 2.5 large deviation rate function using two distinct methods and discusses their relation to fluctuation relations.

Findings

Explicit rate function for level 2.5 large deviations

Comparison of tilting and spectral methods

Connection between fluctuation relations and large deviations

Abstract

We obtain the rate function for the level 2.5 of large deviations for pure jump and diffusion processes. This result is proved by two methods: tilting, for which a tilted process with an appropriate typical behavior is considered, and a spectral method, for which the scaled cumulant generating function is used. We also briefly discuss fluctuation relations, pointing out their connection with large deviations at the level 2.5.