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arXiv:quant-ph/0403040

Comment on "A mathematical theorem as a basis for the second law: Thomson's formulation applied to equilibruim"

Dan Solomon

Published Mar 4, 2004• 0 citations
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Abstract

A.E. Allahverdyan and Th. M. Nieuwenhuizen [1] in their paper "A mathematical theorem as a basis for the second law: Thomson's formulation applied to equilibriium" present a proof of the second law of thermodynamics based on quantum mechanics. In this comment on their paper I offer a counterexample to their proof.
DOI
10.48550/arxiv.quant-ph/0403040

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Recently Allahverdyan and Nieuwenhuizen (cond-mat/0006404) argued that the second law of thermodynamics may be violated in a quantum system as a "consequence of quantum coherence in the presence of the slightly off-equilibrium nature of the bath." By using a standard result about relative entropy, we prove rigorously that the second law is never violated (and, in particular, a perpetual motion of the second kind can never be realized) in quantum systems no matter how strong ``quantum coherence'' is or no matter how far one goes from equilibrium.
Three articles published by the same author in the Revue des Questions Scientifiques in 2005 and 2006 are reexamined with special attention paid to a theorem published by Allahverdyan and Nieuwenhuizen in 2002 concerning Thomson’s formulation of the second law, as well as to the results of the so-called “before-before ” experiment performed on entangled pairs by Stefanov, Zbinden, Gisin and Suarez. As far as thermodynamics are concerned, it is explained here that a macroscopic observer can generate quasi “cycles”, whose cyclical characteristics are in fact only valid from the macroscopic point of view, that can potentially enable her/him to retrieve work from a thermalizer without causing any perpetual motion. Concerning quantum entanglement, it is recognized – in contrast with what the author originally published in 2005 and 2006- that superluminal transmission of decipherable information cannot be achieved if the Copenhagen interpretation of quantum theory remains universally valid. It is also pointed out that the foundations of general relativity cannot be easily reconciled with the implications of Einstein-Podolsky-Rosen measurements.