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Letters in Mathematical Physics

Quantum Thermodynamics – H-Theorem and the Second Law

C. Syros

Published Oct 1, 1999• 1 citation
Publisher
DOI
10.1023/a:1007639410496

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We demonstrate that both Wigner's form of Bell's inequalities as well as a form of the second law of thermodynamics, as manifest in Caratheáodory's principle, can be derived from the same simple experimental and statistical mechanical assumptions combinedwith the trivial behavior of integers. This suggests that Bell's theorem is merely a well-disguised statement of the second law. It also suggests that entanglement is necessary for quantum theory to be in full accord with the second law and thus builds on the results of Wiesniak, Vedral, and Brukner [1] who showed it was necessary for consistency with the third law.
The second law of ordinary thermodynamics and the second law of steady state thermodynamics, as proposed by Oono and Paniconi, are investigated from the microscopic point of view for the open quantum system. Based on the H-theorem of Lindblad, we show that both second laws are consistent with the quantum dynamics generated by the completely positive map. In addition, microscopic expressions of entropy production and ``housekeeping heat'' are obtained for some classes of dynamical quantum systems.