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Nonlinear Kramers equation associated with nonextensive statistical mechanics

G. A. Mendes1, M. S. Ribeiro2, R. S. Mendes3,5, E. K. Lenzi4,5, and F. D. Nobre2,5,*

  • 1Departamento de Física, Universidade Federal do Maranhão, Avenida dos Portugueses 1966, 65080-805 São Luís-MA, Brazil
  • 2Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil
  • 3Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá-PR, Brazil
  • 4Departamento de Física, Universidade Estadual de Ponta Grossa, Avenida Carlos Cavalcanti 4748, 84030-900 Ponta Grossa-PR, Brazil
  • 5National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil

  • *Corresponding author: fdnobre@cbpf.br
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Phys. Rev. E 91, 052106 – Published 5 May, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.052106

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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Phys. Rev. E 91, 052106– Published 5 May, 2015
  • Received 5 March 2015

©2015 American Physical Society

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