Abstract
Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical mechanics should be revised, either on the basis of quantum mechanics or on the basis of general and fundamental considerations about the (in)distinguishability of particles. In this article we argue against this response. We show that both the extensive thermodynamic and the non-extensive statistical entropy are perfectly alright within their own fields of application. Changes in the statistical formulas that remove the discrepancy must be seen as motivated by pragmatic reasons (conventions) rather than as justified by basic arguments about particle statistics.
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Notes
- 1.
A more detailed discussion should also take into account that the division by N! is without significance anyway as long as N is constant: in this case the only effect of the division is that the entropy is changed by a constant term ln N! , see (Versteegh and Dieks 2011).
References
Ben-Naim, A., 2007, “On the So-called Gibbs Paradox, and on the Real Paradox”, in: Entropy 9, pp. 132–136.
Boltzmann, L., 2001, “Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung resp. den Sätzen über das Wärmegleichgewicht”, in: Wissenschaftliche Abhandlungen, Volume II, pp. 164–224. Providence: AMS Chelsea Publishing.
Cheng, C.-H., 2009,“Thermodynamics of the System of Distinguishable Particles”, in: Entropy 11, pp. 326–333.
Dieks, D., 2010, “The Gibbs Paradox Revisited”, in: Explanation, Prediction and Confirmation, edited by D. Dieks et al., pp. 367–377. New York: Springer.
Dieks, D., and Lubberdink, A., 2011, “How Classical Particles Emerge from the Quantum World”, in: Foundations of Physics 41, pp. 1041–1064.
Ehrenfest, P., and Trkal, V., 1920, “Afleiding van het dissociatie-evenwicht uit de theorie der quanta en een daarop gebaseerde berekening van de chemische constanten”, in: Verslagen der Koninklijke Akademie van Wetenschappen, Amsterdam 28, pp. 906-929; “Ableitung des Dissoziationsgleichgewichtes aus der Quantentheorie und darauf beruhende Berechnung der chemischen Konstanten”, in: Annalen der Physik 65, 1921, pp. 609–628.
Fujita, S., 1991, “On the Indistinguishability of Classical Particles”, in: Foundations of Physics 21, pp. 439–457.
Hestenes, D., 1970, “Entropy and Indistinguishability”, in: American Journal of Physics 38, pp. 840–845.
Huang, K., 1963, Statistical Mechanics. New York: Wiley.
Nagle, J. F., 2004, “Regarding the Entropy of Distinguishable Particles”, in: Journal of Statistical Physics 117, pp. 1047–1062.
Saunders, S., 2006, “On the Explanation for Quantum Statistics”, in: Studies in the History and Philosophy of Modern Physics 37, pp. 192–211.
Schrödinger, E., 1948, Statistical Thermodynamics. Cambridge: Cambridge University Press.
Schroeder, D. V., 2000, An Introduction to Thermal Physics. San Francisco: Addison Wesley Longman.
Sommerfeld, A., 1977, Thermodynamik und Statistik. Thun: Deutsch.
Swendsen, R. H., 2002, “Statistical Mechanics of Classical Systems with Distinguishable Particles”, in: Journal of Statistical Physics 107, pp. 1143–1166.
Swendsen, R. H., 2008, “Gibbs’ Paradox and the Definition of Entropy”, in: Entropy 10, pp. 15–18.
Swendsen, R. H., 2012, “Choosing a Definition of Entropy that Works”, in: Foundations of Physics 42, pp. 582–593.
van Kampen, N. G., 1984, “The Gibbs Paradox”, in: W. E. Parry (Ed.), Essays in Theoretical Physics. Oxford: Pergamon Press, pp. 303–312.
Versteegh, M. A. M. and Dieks, D., 2011, “The Gibbs Paradox and the Distinguishability of Identical Particles”, in: American Journal of Physics 79, pp. 741–746.
Wannier, G. H., 1966, Statistical Physics. New York: Wiley.
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Dieks, D. (2013). Is There a Unique Physical Entropy? Micro Versus Macro. In: Andersen, H., Dieks, D., Gonzalez, W., Uebel, T., Wheeler, G. (eds) New Challenges to Philosophy of Science. The Philosophy of Science in a European Perspective, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5845-2_3
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