Maximal work extraction from finite quantum systems

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: 10 June 2004

Abstract

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.