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Validity of nonequilibrium work relations for the rapidly expanding quantum piston

H. T. Quan and Christopher Jarzynski
Phys. Rev. E 85, 031102 – Published 1 March 2012
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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 Schrödinger 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 remain valid at any finite piston speed, provided both components are included, and we study explicitly the work distribution for this model system.

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  • Received 17 August 2011

DOI:https://doi.org/10.1103/PhysRevE.85.031102

©2012 American Physical Society

Synopsis

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Quantum Pistons

Published 1 March 2012

Calculations reveal the relationship between work and free energy for a quantum particle contained in a box with a moving wall.

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Authors & Affiliations

H. T. Quan

  • Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA

Christopher Jarzynski

  • Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA

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Issue

Vol. 85, Iss. 3 — March 2012

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