Fock Space and Field Theoretic Description of Nonequilibrium Work Relations

TL;DR

This paper develops a field theoretic framework for classical particles driven far from equilibrium, deriving fluctuation relations like Jarzynski and Crooks through a gauge symmetry in the Doi-Peliti formalism.

Contribution

It introduces a novel field theory approach to nonequilibrium work relations using Fock space and gauge symmetry, extending fluctuation-dissipation concepts.

Findings

Derivation of Jarzynski and Crooks relations from a gauge invariance

Mapping of particle dynamics to a Doi-Peliti field theory in the continuum limit

Identification of a gauge-like time-reversal symmetry in the field theory

Abstract

We consider classical, interacting particles coupled to a thermal reservoir and subject to a local, time-varying potential while undergoing hops on a lattice. We impose detailed balance on the hopping rates and map the dynamics to the Fock space Doi representation, from which we derive the Jarzynski and Crooks relations. Here the local potential serves to drive the system far from equilibrium and to provide the work. Next, we utilize the coherent state representation to map the system to a Doi-Peliti field theory and take the continuum limit. We demonstrate that time reversal in this field theory takes the form of a gauge-like transformation which leaves the action invariant up to a generated work term. The time-reversal symmetry leads to a fundamental identity, from which we are able to derive the Jarzynski and Crooks relations, as well as a far-from-equilibrium generalization of the fluctuation-dissipation relation.