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$H$-theorem for nonlinear Fokker-Planck equations related to generalized thermostatistics. (English) Zbl 0978.82069
Summary: In correspondence to conventional thermostatistics we formulate an H-theorem showing that transients solutions of nonlinear Fokker-Planck equations related to generalized thermostatistics converge to stationary probability densities. The $H$-theorem is applied to relaxation processes of classical bosons and fermions as proposed by Kaniadakis and Quarati, diffusion processes consistent with the generalized thermostatistics proposed by Tsallis, and stochastic processes with statistical feedback.

MSC:
82C31Stochastic methods in time-dependent statistical mechanics
82C35Irreversible thermodynamics, including Onsager-Machlup theory
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