Reexamination of experimental tests of the fluctuation theorem

TL;DR

This paper critically examines experimental tests of the Fluctuation Theorem and Jarzynski equality, revealing conditions under which they hold or fail, and provides a simplified proof for Langevin dynamics.

Contribution

It offers new insights into the validity of fluctuation relations in experiments and presents a simpler proof for the Fluctuation Theorem applicable to Langevin dynamics.

Findings

Heat exchange obeys the Fluctuation Theorem but not the Jarzynski equality in certain conditions.

Substantial corrections to the Jarzynski equality can occur if force measurement is incomplete.

A simpler proof of the Fluctuation Theorem for Langevin dynamics is provided.

Abstract

The Fluctuation Theorem and the Jarzynski equality are examined in the light of recent experimental tests. For a particle dragged through a solvent, it is shown that $Q,$ the heat exchanged with the reservoir, obeys the asymptotic Fluctuation Theorem but not the Jarzynski equality, due to slowly decaying tails in its distribution. For molecular stretching experiments, substantial corrections to the Jarzynski equality can result from not measuring the force at the end of the molecule that is moved. We also present a proof of the Fluctuation Theorem for Langevin dynamics that is considerably simpler than the standard proof.