Journal Article

Is - <i>k</i>Tr(ρlnρ) the entropy in quantum mechanics

OR Shenker

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 50, issue 1, pages 33-48
Published in print March 1999 | ISSN: 0007-0882
Published online March 1999 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/50.1.33
Is - kTr(ρlnρ) the entropy in quantum mechanics

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In quantum mechanics, the expression for entropy is usually taken to be -kTr(ρlnρ), where ρ is the density matrix. The convention first appears in Von Neumann's Mathematical Foundations of Quantum Mechanics. The argument given there to justify this convention is the only one hitherto offered. All the arguments in the field refer to it at one point or another. Here this argument is shown to be invalid. Moreover, it is shown that, if entropy is -kTr(ρlnρ), then perpetual motion machines are possible. This and other considerations support the conclusion that this expression is not the quantum-mechanical correlate of thermodynamic entropy. Its usefulness in quantum-statistical mechanics can be explained by its being a convenient quantification of information, but information and entropy are not synonymous. As the present paper shows, one can change while the other is conserved.

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Subjects: Philosophy of Science ; Science and Mathematics

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