The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences

TL;DR

This paper derives a generalized fluctuation theorem for far-from-equilibrium systems and uses it to provide a concise proof of the nonequilibrium work relation connecting work measurements to free energy differences.

Contribution

It introduces a generalized fluctuation theorem for stochastic, microscopically reversible dynamics and links it to the nonequilibrium work relation.

Findings

Derived a generalized fluctuation theorem for nonequilibrium systems.

Provided a succinct proof of the nonequilibrium work relation.

Established a theoretical foundation connecting entropy production and free energy differences.

Abstract

There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far-from-equilibrium expression relates nonequilibrium measurements of the work done on a system to equilibrium free energy differences. In this paper, we derive a generalized version of the fluctuation theorem for stochastic, microscopically reversible dynamics. Invoking this generalized theorem provides a succinct proof of the nonequilibrium work relation.