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Nonlinear Ehrenfest's urn model

G. A. Casas*, F. D. Nobre†, and E. M. F. Curado‡

  • Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil

  • *Corresponding author: gabrielaa@cbpf.br
  • †fdnobre@cbpf.br
  • ‡evaldo@cbpf.br
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Phys. Rev. E 91, 042139 – Published 28 April, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.042139

Abstract

Ehrenfest's urn model is modified by introducing nonlinear terms in the associated transition probabilities. It is shown that these modifications lead, in the continuous limit, to a Fokker-Planck equation characterized by two competing diffusion terms, namely, the usual linear one and a nonlinear diffusion term typical of anomalous diffusion. By considering a generalized H theorem, the associated entropy is calculated, resulting in a sum of Boltzmann-Gibbs and Tsallis entropic forms. It is shown that the stationary state of the associated Fokker-Planck equation satisfies precisely the same equation obtained by extremization of the entropy. Moreover, the effects of the nonlinear contributions on the entropy production phenomenon are also analyzed.

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Phys. Rev. E 91, 042139– Published 28 April, 2015
  • Received 2 December 2014

©2015 American Physical Society

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