Mathematical Solution of the Gibbs Paradox V
ISSN 0001-4346, Mathematical Notes, 2011, Vol. 89, No. 2, pp. 266–276. © Pleiades Publishing, Ltd., 2011. Original Russian Text © V. P. Maslov, 2011, published in Matematicheskie Zametki, 2011, Vol. 89, No. 2, pp. 272–284. Mathematical Solution of the Gibbs Paradox V. P. Maslov * Moscow State University Received December 20, 2010 Abstract—In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it. DOI: 10.1134/S0001434611010329 Keywords: Zeno line, partitio numerorum, phase transition, cluster, dimer, critical tempera- ture, Boyle temperature, jamming effect, Bose–Einstein distribution, Gibbs paradox. Since all the papers of the author dealing with this problem1 were published in English, here we present a short survey of these papers in both Russian and English. The Gibbs paradox has been a stumbling block for many physicists, including Einstein, Gibbs, Planck, Fermi, and many others (15 Nobel laureates in physics studied this problem) as well as for two great mathematicians Von Neumann and Poincare.´ Poincare´ did not obtain the mathematical solution of the Gibbs paradox, but attempted to solve this problem from the philosophical point of view.2 A careful analysis of Poincare’s´ philosophy shows that it is especially constructed so as to justify the contradiction between two physical theories. He writes, in particular, “If a physicist finds a contradiction between two theories that are equally dear to him, he will sometimes say: let’s not worry about this; the intermediate links of the chain may be hidden from us, but we will strongly hold on to its extremities.
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