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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.

References

Bennett, C. 1973. “Logical Reversibility of Computation.” IBM Journal of Research and Development 17 (6): 525–32.CrossRefGoogle Scholar
Earman, J., and Norton, J. D. 1999. “Exorcist XIV: The Wrath of Maxwell’s Demon.” Pt. 2, “From Szilard to Landauer and Beyond.” Studies in History and Philosophy of Science B 30(1): 1–40.Google Scholar
Einstein, A. 1914. “Beiträge zur Quantentheorie.” Verhandlungen der Deutschen Physikalischen Gesellschaft 12.Google Scholar
Hemmo, M., and Shenker, O. R. 2006. “Von Neumann’s Entropy Does Not Correspond to Thermodynamic Entropy.” Philosophy of Science 73 (2): 153–74.CrossRefGoogle Scholar
Hemmo, M., and Shenker, O. R. 2012. The Road to Maxwell’s Demon: Conceptual Foundations of Statistical Mechanics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Henderson, L. 2003. “The Von Neumann Entropy: A Reply to Shenker.” British Journal for the Philosophy of Science 54 (2): 291–96.CrossRefGoogle Scholar
Ladyman, J., Presnell, S., Short, A. J., and Groisman, B. 2007. “The Connection between Logical and Thermodynamic Irreversibility.” Studies in History and Philosophy of Science B 38 (1): 58–79.CrossRefGoogle Scholar
Ladyman, J., and Robertson, K. 2013. “Landauer Defended: Reply to Norton.” Studies in History and Philosophy of Science B 44 (3): 263–71.Google Scholar
Landauer, R. 1961. “Irreversibility and Heat Generation in the Computing Process.” IBM Journal of Research and Development 5 (3): 183–91.CrossRefGoogle Scholar
Maroney, O. J. 2009a. “Generalizing Landauer’s Principle. Physical Review E 79 (3): 031105.Google Scholar
Maroney, O. J. 2009b. “Information Processing and Thermodynamic Entropy.” In Stanford Encyclopedia of Philosophy, ed. Zalta, E. N. Stanford, CA: Stanford University. https://plato.stanford.edu/entries/information-entropy/.Google Scholar
Maxwell, J. 1878. “Diffusion.” In Encyclopedia Britannica. 9th ed., vol. 7, 214–21.Google Scholar
Maxwell, J. C. 1995. Maxwell on Heat and Statistical Mechanics: On “Avoiding All Personal Enquiries” of Molecules, ed. Garber, E., Brush, S. G., and Everitt, C. W. F. Bethlehem, PA: Lehigh University Press.Google Scholar
Myrvold, W. C. 2011. “Statistical Mechanics and Thermodynamics: A Maxwellian View.” Studies in History and Philosophy of Science B 42 (4): 237–43.Google Scholar
Norton, J. D. 2011. “Waiting for Landauer.” Studies in History and Philosophy of Science B 42 (3): 184–98.Google Scholar
Norton, J. D. 2013. “All Shook Up: Fluctuations, Maxwell’s Demon and the Thermodynamics of Computation.” Entropy 15 (10): 4432–83.CrossRefGoogle Scholar
Planck, M. 1991. Treatise on Thermodynamics. 7th ed. New York: Dover.Google Scholar
Shenker, O. R. 1999. “Is −kTr(ρlnρ) the Entropy in Quantum Mechanics?” British Journal for the Philosophy of Science 50 (1): 33–48.CrossRefGoogle Scholar
Szilard, L. 1929. “Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen” [On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings]. Zeitschrift fur Physik 53:840–56.CrossRefGoogle Scholar
von Neumann, J. 1955. Mathematical Foundations of Quantum Mechanics. Trans. Beyer, E. T. Princeton, NJ: Princeton University Press.Google Scholar
von Neumann, J. 1996. Mathematische Grundlagen der Quantenmechanik. 2nd ed. Dordrecht: Springer.CrossRefGoogle Scholar
Wallace, D. 2014. “Thermodynamics as Control Theory.” Entropy 16 (2): 699–725.CrossRefGoogle Scholar