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  • Title: Nonlinear Kramers equation associated with nonextensive statistical mechanics.
    Author: Mendes GA, Ribeiro MS, Mendes RS, Lenzi EK, Nobre FD.
    Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2015 May; 91(5):052106. PubMed ID: 26066118.
    Abstract:
    Stationary and time-dependent solutions of a nonlinear Kramers equation, as well as its associated nonlinear Fokker-Planck equations, are investigated within the context of Tsallis nonextensive statistical mechanics. Since no general analytical time-dependent solutions are found for such a nonlinear Kramers equation, an ansatz is considered and the corresponding asymptotic behavior is studied and compared with those known for the standard linear Kramers equation. The H-theorem is analyzed for this equation and its connection with Tsallis entropy is investigated. An application is discussed, namely the motion of Hydra cells in two-dimensional cellular aggregates, for which previous measurements have verified q-Gaussian distributions for velocity components and superdiffusion. The present analysis is in quantitative agreement with these experimental results.
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