Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale

TL;DR

This paper introduces two novel approaches to derive Generalized Fluctuation-Dissipation Theorems for Markov processes, utilizing stochastic derivatives and exponential martingales, extending the scope beyond traditional diffusion and jump processes.

Contribution

It presents original methods using stochastic derivatives and exponential martingales to establish GFDT and Fluctuation Relations for general Markov processes.

Findings

Proves GFDT and FR for broad classes of Markov processes.

Links Fluctuation Relations to exponential martingales.

Extends fluctuation theorems beyond diffusion and jump processes.

Abstract

In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales functionals. We show that GFDT are perturbative versions of relations verified by these exponential martingales. Along the way, we prove GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the usual proof for diffusion and pure jump processes. Finally, we relate the FR to a family of backward and forward exponential martingales.