Generalized Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac and Acharya-Swamy Statistics and the Polya Urn Model

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dc.creatorNiven, Robert K.
dc.creatorGrendar, Marian
dc.date2008-08-15
dc.date.accessioned2026-07-07T09:56:53Z
dc.date.available2026-07-07T09:56:53Z
dc.descriptionGeneralized probability distributions for Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, with unequal source probabilities $q_i$ for each level $i$, are obtained by combinatorial reasoning. For equiprobable degenerate sublevels, these reduce to those given by Brillouin in 1930, more commonly given as a statistical weight for each statistic. These distributions and corresponding cross-entropy (divergence) functions are shown to be special cases of the Pólya urn model, involving neither independent nor identically distributed ("ninid") sampling. The most probable Pólya distribution contains the Acharya-Swamy intermediate statistic.
dc.description8 pages; 4 figures
dc.identifierhttps://arxiv.org/abs/0808.2102
dc.identifierhttp://arxiv.org/abs/0808.2102
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167138
dc.subjectStatistical Mechanics
dc.titleGeneralized Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac and Acharya-Swamy Statistics and the Polya Urn Model
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