The Jarzynski relation, fluctuation theorems, and stochastic thermodynamics for non-Markovian processes

2007/09/14 by Thomas Speck, Udo Seifert · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computer science #Entropy (arrow of time) #Entropy production #Ergodic theory #Fluctuation theorem #Markov process #Mathematics #Non-equilibrium thermodynamics #Nonlinear system #Physics #Pure mathematics #Quantum Mechanics and Applications #Quantum mechanics #Relation (database) #Stationary state #Statistical Mechanics and Entropy #Statistical physics #Stochastic process #Thermodynamics #cond-mat.stat-mech

paper · pdf · doi:10.1088/1742-5468/2007/09/l09002

published as J. Stat. Mech. L09002 (2007) · Accepted for publication in JSM

arxiv created 2007/09/14 · openalex publication_date 2007/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Distribution of work in isothermal nonequilibrium processes
• Path-ensemble averages in systems driven far from equilibrium
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Work probability distribution in single-molecule experiments
• The Nonequilibrium Thermodynamics of Small Systems

Cited by

• Energy representation for nonequilibrium Brownian-like systems: Steady states and fluctuation relations