Fluctuation symmetries for work and heat

TL;DR

This paper investigates fluctuation symmetries in work and heat for a particle driven by a time-dependent potential, establishing conditions for exact symmetry and analyzing corrections due to boundary terms.

Contribution

It provides conditions under which fluctuation symmetries hold exactly for work and heat in Langevin systems with time-dependent protocols.

Findings

Exact fluctuation symmetry for work under specific conditions.

Counterexamples where symmetry does not hold without these conditions.

A corrected fluctuation symmetry for heat considering boundary effects.

Abstract

We consider a particle dragged through a medium at constant temperature as described by a Langevin equation with a time-dependent potential. The time-dependence is specified by an external protocol. We give conditions on potential and protocol under which the dissipative work satisfies an exact symmetry in its fluctuations for all times. We also present counter examples to that exact fluctuation symmetry when our conditions are not satisfied. Finally, we consider the dissipated heat which differs from the work by a temporal boundary term. We explain when and why there can be a correction to the standard fluctuation theorem due to the unboundedness of that temporal boundary. However, the corrected fluctuation symmetry has again a general validity.