A proof of Jarzynski's non-equilibrium work theorem for dynamical systems that conserve the canonical distribution

TL;DR

This paper provides a rigorous derivation of the Jarzynski identity and Crooks fluctuation theorem for deterministic systems that preserve the canonical distribution, expanding their applicability to various Hamiltonian and thermostatted dynamics.

Contribution

It offers a novel proof of fluctuation theorems for a broad class of deterministic dynamics conserving the canonical distribution.

Findings

Derivation of Jarzynski identity for Hamiltonian and thermostatted systems

Extension of Crooks fluctuation theorem to deterministic dynamics

Relation between heat absorption and phase flow Jacobian

Abstract

We present a derivation of the Jarzynski identity and the Crooks fluctuation theorem for systems governed by deterministic dynamics that conserves the canonical distribution such as Hamiltonian dynamics, Nose-Hoover dynamics, Nose-Hoover chains and Gaussian isokinetic dynamics. The proof is based on a relation between the heat absorbed by the system during the non-equilibrium process and the Jacobian of the phase flow generated by the dynamics.