A field-theoretic approach to nonequilibrium work identities

TL;DR

The paper develops a field-theoretic framework for nonequilibrium work identities in a space-time field governed by Model A dynamics. Using a Martin-Siggia-Rose path integral with a four-field dynamical action, it shows that Jarzynski's equality emerges from dynamical invariances, and it derives a generalized, nonstationary fluctuation-dissipation relation via Ward-Takahashi identities. A central insight is that equilibrium supersymmetry, encoded in BRST transformations, underpins both equilibrium fluctuation-dissipation relations and nonequilibrium work identities; for time-dependent drives, adding the Jarzynski term partially restores this symmetry and makes Jarzynski's theorem a consequence of the corresponding Ward-Takahashi identities. The approach offers a unifying perspective on equilibrium and nonequilibrium thermodynamics for extended systems and points to experimental tests and extensions to more complex stochastic models.

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.