Validity of nonequilibrium work relations for the rapidly expanding quantum piston

TL;DR

This paper investigates the validity of quantum nonequilibrium work relations during rapid expansions of a quantum piston, demonstrating their robustness when all wave function components are considered.

Contribution

It provides an exact analysis showing that quantum work relations hold for a rapidly expanding piston when both static and dynamic wave components are included.

Findings

Work relations remain valid at any piston speed.

Wave function decomposition into static and dynamic parts is crucial.

Explicit work distribution for the quantum piston is derived.

Abstract

Recent work by Teifel and Mahler [Eur. Phys. J. B 75, 275 (2010)] raises legitimate concerns regarding the validity of quantum nonequilibrium work relations in processes involving moving hard walls. We study this issue in the context of the rapidly expanding one-dimensional quantum piston. Utilizing exact solutions of the time-dependent Schrodinger equation, we find that the evolution of the wave function can be decomposed into static and dynamic components, which have simple semiclassical interpretations in terms of particle-piston collisions. We show that nonequilibrium work relations remains valid at any finite piston speed, provided both components are included, and we study explicitly the work distribution for this model system.