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On the Equivalence of von Neumann and Thermodynamic Entropy

Published online by Cambridge University Press:  01 January 2022

Carina E. A. Prunkl
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Abstract

In 1932, John von Neumann argued for the equivalence of the thermodynamic entropy and −Trρlnρ, since known as the von Neumann entropy. Meir Hemmo and Orly R. Shenker recently challenged this argument by pointing out an alleged discrepancy between the two entropies in the single-particle case, concluding that they must be distinct. In this article, their argument is shown to be problematic as it (a) allows for a violation of the second law of thermodynamics and (b) is based on an incorrect calculation of the von Neumann entropy.

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Articles
Information
Philosophy of Science , Volume 87 , Issue 2 , April 2020 , pp. 262 - 280
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

I thank Christopher Timpson (University of Oxford), Harvey Brown (University of Oxford), Owen Maroney (University of Oxford), Katie Robertson, David Wallace (University of Southern California), and James Ladyman (University of Bristol) for helpful discussions and two anonymous referees for useful comments. This work was supported by the British Society for the Philosophy of Science, the University of Oxford, the Black Hole Initiative, and the John Templeton Foundation.

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