Nonlinear Kramers equation associated with nonextensive statistical mechanics

Nonlinear Kramers equation associated with nonextensive statistical mechanics

G. A. Mendes, M. S. Ribeiro, R. S. Mendes, E. K. Lenzi, and F. D. Nobre, Phys. Rev. E 91, 052106 (2015), PDF | DOI

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.