Nonequilibrium work statistics of an Aharonov-Bohm flux

TL;DR

This paper studies the work statistics of a noninteracting electron gas in a ring with a magnetic flux, showing how quantum and classical regimes differ in work distribution and Jarzynski equality applicability.

Contribution

It demonstrates that the Jarzynski equality holds with the grand potential for a noninteracting electron gas under a changing magnetic flux, highlighting quantum and classical differences.

Findings

Work distribution is Gaussian at high temperatures.

Quantum regime shows a finite free energy difference.

Work statistics depend on the number of electrons.

Abstract

We investigate the statistics of work performed on a noninteracting electron gas confined into a ring as a threaded magnetic field is turned on. For an electron gas initially prepared in a grand canonical state it is demonstrated that the Jarzynski equality continues to hold in this case, with the free energy replaced by the grand potential. The work distribution displays a marked dependence on the temperature. While in the classical (high temperature) regime, the work probability density function follows a Gaussian distribution and the free energy difference entering the Jarzynski equality is null, the free energy difference is finite in the quantum regime, and the work probability distribution function becomes multimodal. We point out the dependence of the work statistics on the number of electrons composing the system.