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Representing Mixtures

Published online by Cambridge University Press:  27 March 2023

James Wills
James Wills*
Affiliation:
Pembroke College, Oxford, UK
*
Email: [email protected]
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Abstract

I describe two candidate representations of a mixture. The first, which I call the standard representation, is not a good representation of a mixture in spite of its widespread popularity. The second, which I call Gibbs’s representation, is less widely adopted but is, I argue, a much better representation. I show that once we have a precise mathematical structure that can be used to represent thermodynamic systems, and once an adequate perspective on representation is adopted, Gibbs’s representation trumps the standard representation.

Type
Article
Information
Philosophy of Science , Volume 90 , Issue 3 , July 2023 , pp. 558 - 579
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of the Philosophy of Science Association

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References

Adkins, Clement John. 1983. Equilibrium Thermodynamics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Arnold, Vladimir Igorevich. 1990. “Contact Geometry: The Geometrical Method of Gibbs’s Thermodynamics.” In Proceedings of the Gibbs Symposium: Yale University, May 15-17, 1989, edited by Daniel G. Caldi and George D. Mostow, 163-80. Providence, RI: American Mathematical Society.Google Scholar
Baierlein, Ralph. 1971. Atoms and Information Theory: An Introduction to Statistical Mechanics. San Francisco: W. H. Freeman.Google Scholar
Belot, Gordon. 2018. “Fifty Million Elvis Fans Can’t Be Wrong.” Nous 52 (4): 946–81.CrossRefGoogle Scholar
Blundell, Stephen J., and Blundell, Katherine M.. 2010. Concepts in Thermal Physics. 2nd ed. Oxford: Oxford University Press.Google Scholar
Brown, Harvey R., and Uffink, Jos. 2001. “The Origins of Time-Asymmetry in Thermodynamics: The Minus First Law.” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (4): 525–38.CrossRefGoogle Scholar
Burke, William L. 1985. Applied Differential Geometry. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Callen, Herbert B. 1960. Thermodynamics. New York: John Wiley & Sons.Google Scholar
Darrigol, Olivier. 2018. “The Gibbs Paradox: Early History and Solutions.” Entropy 20 (6): 443.CrossRefGoogle ScholarPubMed
Dieks, Dennis. 2018. “The Gibbs Paradox and Particle Individuality.” Entropy 20 (6): 466.CrossRefGoogle ScholarPubMed
Fletcher, Samuel C. 2020. “On Representational Capacities, with an Application to General Relativity.” Foundations of Physics 50 (4): 228–49.CrossRefGoogle Scholar
Frigg, Roman, and Nguyen, James. 2020. Modelling Nature: An Opinionated Introduction to Scientific Representation. Cham, Switzerland: Springer.CrossRefGoogle Scholar
Gibbs, Josiah Willard. 1878. “On the Equilibrium of Heterogeneous Substances.” In Transactions of the Connecticut Academy of Arts and Sciences, 108-248, 343-524. New Haven, CT: Connecticut Academy.Google Scholar
Halvorson, Hans. 2019. The Logic in Philosophy of Science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hermann, Robert. 1973. Geometry, Physics, and Systems. New York: Marcel Dekker.Google Scholar
Jaynes, Edwin Thompson. 1992. “The Gibbs Paradox.” In Maximum-Entropy and Bayesian Methods, edited by Ray Smith, C., Gary, J. Erickson, and Neudorfer, Paul, 1–21. Dordrecht: Kluwer.Google Scholar
Kondepudi, Dilip, and Prigogine, Ilya. 1998. Modern Thermodynamics: From Heat Engines to Dissipative Structures. Hoboken, NJ: John Wiley & Sons.Google Scholar
Lieb, Elliot H., and Yngvason, Jakob. 1999. “The Physics and Mathematics of the Second Law of Thermodynamics.” Physics Reports 310 (1): 1–96.CrossRefGoogle Scholar
Mrugała, Ryszard. 1978. “Geometrical Formulation of Equilibrium Phenomenological Thermodynamics.” Reports on Mathematical Physics 14 (3): 419–27.CrossRefGoogle Scholar
Mrugała, Ryszard. 2000. “Geometrical Methods in Thermodynamics.” In Thermodynamics of Energy Conversion and Transport, edited by Sieniutycz, Stanislaw and De Vos, Alexis, 257–85. New York: Springer.CrossRefGoogle Scholar
Planck, Max. 1903. Treatise on Thermodynamics. Translated by Ogg, Alexander. London: Longmans, Green & Co.Google Scholar
Pooley, Oliver. 2021. “The Hole Argument.” In The Routledge Companion to the Philosophy of Physics, edited by Knox, Eleanor and Wilson, Alastair, 145–59. New York: Routledge.CrossRefGoogle Scholar
Roberts, Bryan W. 2020. “Regarding ‘Leibniz Equivalence’.” Foundations of Physics 50 (4): 250–69.CrossRefGoogle Scholar
Saunders, Simon. 2018. “The Gibbs Paradox.” Entropy 20 (8): 552.CrossRefGoogle ScholarPubMed
Sears, Francis W., and Salinger, Gerhard L.. 1975. Thermodynamics, Kinetic Theory, and Statistical Thermodynamics. Boston: Addison-Wesley.Google Scholar
Tisza, László. 1966. Generalized Thermodynamics. Cambridge, MA: MIT Press.Google Scholar
Tisza, László. 1961. “The Thermodynamics of Phase Equilibrium.” Annals of Physics 13 (1): 1–92.CrossRefGoogle Scholar
Uffink, Jos. 2001. “Bluff Your Way in the Second Law of Thermodynamics.” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (3): 305–94.CrossRefGoogle Scholar
van Kampen, N. G. 1984. “The Gibbs Paradox.” In Essays in Theoretical Physics in Honour of Dirk ter Haar, edited by Parry, William Edward, 303-12. Oxford: Pergamon Press.CrossRefGoogle Scholar
van Lith, Janneke. 2018. “The Gibbs Paradox: Lessons from Thermodynamics.” Entropy 20 (5): 328.CrossRefGoogle ScholarPubMed
Weatherall, James Owen. 2018. “Regarding the ‘Hole Argument’.” British Journal for the Philosophy of Science 69 (2): 329–50.CrossRefGoogle Scholar
Wills, James. 2022. “Identity and Indistinguishability in Thermal Physics.” PhD diss., London School of Economics and Political Science.Google Scholar