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Updated: Apr 12, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Nonlinear Ehrenfest's urn model
G A Casas1, F D Nobre1, E M F Curado1
1Centro 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.
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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