Europhys. Lett.
Volume 67, Number 4, August 2004
Page(s) 565 - 571
Section General
Published online 01 August 2004
Europhys. Lett., 67 (4), pp. 565-571 (2004)
DOI: 10.1209/epl/i2004-10101-2

Maximal work extraction from finite quantum systems

A. E. Allahverdyan1, 2, R. Balian3 and Th. M. Nieuwenhuizen1

1  Institute for Theoretical Physics - Valckenierstraat 65 1018 XE Amsterdam, The Netherlands
2  Yerevan Physics Institute - Alikhanian Brothers St. 2, Yerevan 375036, Armenia
3  SPhT, CEA-Saclay - 91191 Gif-sur-Yvette cedex, France

(Received 22 March 2004; accepted in final form 10 June 2004)

Thermodynamics teaches that if a system initially off-equilibrium is coupled to work sources, the maximum work that it may yield is governed by its energy and entropy. For finite systems this bound is usually not reachable. The maximum extractable work compatible with quantum mechanics ("ergotropy") is derived and expressed in terms of the density matrix and the Hamiltonian. It is related to the property of majorization: more major states can provide more work. Scenarios of work extraction that contrast the thermodynamic intuition are discussed, e.g. a state with larger entropy than another may produce more work, while correlations may increase or reduce the ergotropy.

05.70.Ln - Nonequilibrium and irreversible thermodynamics.
05.30.-d - Quantum statistical mechanics.
82.60.Qr - Thermodynamics of nanoparticles.

© EDP Sciences 2004