Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes

TL;DR

This paper extends fundamental non-equilibrium thermodynamic relations, including the Jarzynski relation and Crooks relation, to non-Markovian stochastic processes with memory, broadening their applicability beyond Markovian systems.

Contribution

It provides a rigorous proof of the Jarzynski relation for non-Markovian processes with stationary states, and demonstrates how stochastic thermodynamics concepts apply to these systems.

Findings

Proves Jarzynski relation for non-Markovian processes with stationary states

Derives Crooks relation and fluctuation theorem for entropy production in non-Markovian dynamics

Establishes the applicability of stochastic thermodynamics to systems with memory

Abstract

We prove the Jarzynski relation for general stochastic processes including non-Markovian systems with memory. The only requirement for our proof is the existence of a stationary state, therefore excluding non-ergodic systems. We then show how the concepts of stochastic thermodynamics can be used to prove further exact non-equilibrium relations like the Crooks relation and the fluctuation theorem on entropy production for non-Markovian dynamics.