Transient State Work Fluctuation Theorem for a Driven Classical System

TL;DR

This paper derives a general transient state work fluctuation theorem and Jarzynski equality for a driven classical harmonic oscillator coupled to a harmonic heat bath, including non-Markovian dynamics.

Contribution

It provides a derivation applicable to both Markovian and non-Markovian baths without spectral restrictions, extending fluctuation theorems to more general systems.

Findings

Derivation of a transient work fluctuation theorem for non-Markovian systems

Extension of the Jarzynski equality to non-Markovian harmonic oscillators

General framework applicable to a wide class of classical driven systems

Abstract

We derive the nonequilibrium transient state work fluctuation theorem and also the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics not only dissipative but also non-Markovian in general. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not only restricted to the Markovian bath rather it is more general, for a non-Markovian bath.