A field-theoretic approach to nonequilibrium work identities

TL;DR

This paper develops a field-theoretic framework for nonequilibrium work relations, deriving exact identities and symmetries that extend fluctuation-dissipation relations to non-stationary systems, with potential experimental applications.

Contribution

It introduces a novel field-theoretic approach to derive and generalize nonequilibrium work identities, linking Jarzynski's equality to symmetries and supersymmetry in stochastic dynamics.

Findings

Derived Jarzynski's equality via dynamical symmetries.

Generalized fluctuation-dissipation relations for non-stationary states.

Connected work identities to Ward-Takahashi identities.

Abstract

We study nonequilibrium work relations for a space-dependent field with stochastic dynamics (Model A). Jarzynski's equality is obtained through symmetries of the dynamical action in the path integral representation. We derive a set of exact identities that generalize the fluctuation-dissipation relations to non-stationary and far-from-equilibrium situations. These identities are prone to experimental verification. Furthermore, we show that a well-studied invariance of the Langevin equation under supersymmetry, which is known to be broken when the external potential is time-dependent, can be partially restored by adding to the action a term which is precisely Jarzynski's work. The work identities can then be retrieved as consequences of the associated Ward-Takahashi identities.