A work fluctuation theorem for a Brownian particle in a non confining potentia

TL;DR

This paper derives a work fluctuation theorem for Brownian particles in nonconfining potentials, revealing a lower bound on work and an additional energy term absent in confining cases.

Contribution

It introduces a new fluctuation theorem applicable to nonconfining potentials, extending the Jarzynski equality to unbounded diffusive systems.

Findings

Establishes a lower bound on average work in nonconfining potentials

Identifies an extra energy term due to diffusive expansion

Extends fluctuation theorems beyond confining systems

Abstract

Using the Feynman-Kac formula, a work fluctuation theorem for a Brownian particle in a nonconfining potential, e.g., a potential well with finite depth, is derived. The theorem yields aninequality that puts a lower bound on the average work needed to change the potential in time.In comparison to the Jarzynski equality, which holds for confining potentials, an additional termdescribing a form of energy related to the never ending diffusive expansion appears.