ISSN:
1434-6036
Keywords:
PACS. 66.10.Cb Diffusion and thermal diffusion - 05.20.-y Classical statistical mechanics - 05.60.-k Transport processes
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract: Nonlinear Fokker-Planck equations (e.g., the diffusion equation for porous medium) are important candidates for describing anomalous diffusion in a variety of systems. In this paper we introduce such nonlinear Fokker-Planck equations with general state-dependent diffusion, thus significantly generalizing the case of constant diffusion which has been discussed previously. An approximate maximum entropy (MaxEnt) approach based on the Tsallis nonextensive entropy is developed for the study of these equations. The MaxEnt solutions are shown to preserve the functional relation between the time derivative of the entropy and the time dependent solution. In some particular important cases of diffusion with power-law multiplicative noise, our MaxEnt scheme provides exact time dependent solutions. We also prove that the stationary solutions of the nonlinear Fokker-Planck equation with diffusion of the (generalized) Stratonovich type exhibit the Tsallis MaxEnt form.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s100510051006
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