4.5 Article

Generalized classical, quantum and intermediate statistics and the Polya urn model

Journal

PHYSICS LETTERS A
Volume 373, Issue 6, Pages 621-626

Publisher

ELSEVIER
DOI: 10.1016/j.physleta.2008.12.025

Keywords

Entropy; Combinatorial; Statistical mechanics; Boltzmann principle; MaxProb; Quantum mechanics; Intermediate statistics

Funding

  1. Marie Curie Incoming International Fellowship [039729]
  2. European Commission
  3. VEGA [1/3016/06]
  4. Australian Research Council [DP0210999]
  5. Australian Research Council [DP0210999] Funding Source: Australian Research Council

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Generalized probability distributions for Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, with unequal source (prior) 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 Polya urn model, involving neither independent nor identically distributed (ninid) sampling. The most probable Polya distribution is shown to contain the Acharya-Swamy intermediate statistic. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.

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