Abstract
A probabilistic derivation of van der Waals' equation is given where the non-ideal contributions to the entropy coincide with the log-likelihood ratios, at their maxima, of the binomial distribution and the upper or lower bounds on the hypergeometric and Pólya distributions. The hypergeometric distribution accounts for the repulsive interactions of a hard sphere gas while the Pólya distribution accounts for the attractive interactions.
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1. Work supported in part by contributions from the Ministry of Public Education (M.P.I.) and the National Science Council (C.N.R.).
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Lavenda, B.H. Probabilistic derivation of van der Waals' equation. Found Phys Lett 3, 285–290 (1990). https://doi.org/10.1007/BF00666018
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DOI: https://doi.org/10.1007/BF00666018