Is - kTr( ln ) the entropy in quantum mechanics

British Journal for the Philosophy of Science 50 (1):33-48 (1999)
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In quantum mechanics, the expression for entropy is usually taken to be -kTr(ln), where 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(ln), 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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Orly Shenker
Hebrew University of Jerusalem

Citations of this work

Quantum Foundations of Statistical Mechanics and Thermodynamics.Orly Shenker - 2021 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. Oxford: Routledge. pp. Ch. 29.
Information vs. entropy vs. probability.Orly Shenker - 2019 - European Journal for Philosophy of Science 10 (1):1-25.
How to spell out the epistemic conception of quantum states.Simon Friederich - 2011 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (3):149-157.
Can We Explain Thermodynamics By Quantum Decoherence?Meir Hemmo & Orly Shenker - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (4):555-568.

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