Casas G A, Nobre F D, Curado E M F
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.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042139. doi: 10.1103/PhysRevE.91.042139. Epub 2015 Apr 28.
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.
通过在相关转移概率中引入非线性项，对埃伦费斯特瓮模型进行了修改。结果表明，在连续极限情况下，这些修改会导致一个福克 - 普朗克方程，该方程由两个相互竞争的扩散项表征，即通常的线性扩散项和一个典型的反常扩散非线性扩散项。通过考虑一个广义的H定理，计算了相关的熵，得到了玻尔兹曼 - 吉布斯熵形式和Tsallis熵形式的总和。结果表明，相关福克 - 普朗克方程的稳态精确地满足通过熵极值化得到的相同方程。此外，还分析了非线性贡献对熵产生现象的影响。
