A general nonlinear Fokker-Planck equation and its associated entropy |
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Authors: | V Schwämmle E MF Curado F D Nobre |
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Institution: | (1) Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de Janeiro, RJ, 22290-180, Brazil |
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Abstract: | A recently introduced nonlinear Fokker-Planck equation, derived
directly from a master equation, comes out as a very
general tool to describe phenomenologically systems presenting complex
behavior, like anomalous diffusion, in the presence of
external forces. Such an equation is characterized by a nonlinear diffusion
term that may present, in general, two distinct powers of the probability
distribution. Herein, we calculate the stationary-state distributions
of this equation in some special cases, and introduce associated classes of
generalized entropies in order to satisfy the H-theorem. Within this approach, the parameters associated with the transition
rates of the original master-equation are related to such
generalized entropies, and are shown to obey some restrictions. Some
particular cases are discussed. |
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Keywords: | PACS" target="_blank">PACS 05 40 Fb Random walks and Levy flights 05 20 -y Classical statistical mechanics 05 40 Jc Brownian motion 66 10 Cb Diffusion and thermal diffusion |
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