By Numénius, E. des Places
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1143-1166. Swendsen, R. , 2008, “Gibbs’ Paradox and the Deﬁnition of Entropy”, in: Entropy 10, pp. 15-18. Swendsen, R. , 2012, “Choosing a Deﬁnition of Entropy that Works”, in: Foundations of Physics 42, pp. 582-593. van Kampen, N. , 1984, “The Gibbs Paradox”, in: W. E. ), Essays in Theoretical Physics. Oxford: Pergamon Press, pp. 303-312. Versteegh, M. A. M. , 2011, “The Gibbs Paradox and the Distinguishability of Identical Particles”, in: American Journal of Physics 79, pp. 741-746. Wannier, G.
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These factorials are important in statistical mechanics, for example in predicting what happens in mixing processes. But it was already argued by Ehrenfest and Trkal (1920, 1921; see also van Kampen 1984) that these factorials can be understood within the standard formalism and do not require a change in the formula S = k ln W for closed systems. Indeed, the dependence of the total entropy in Eq. (2) on N1 and N2 is unrelated to how N occurs in this formula (and to the choice of the zero of the total entropy).