title: Nonlinear Kramers equation associated with nonextensive statistical mechanics.
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.
authors.affiliation: Departamento de Física, Universidade Federal do Maranhão, Avenida dos Portugueses 1966, 65080-805 São Luís-MA, Brazil.
authors.forename: G A
authors.initials: GA
authors.lastname: Mendes
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil.
authors.forename: M S
authors.initials: MS
authors.lastname: Ribeiro
authors.affiliation: Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá-PR, Brazil.|National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil.
authors.forename: R S
authors.initials: RS
authors.lastname: Mendes
authors.affiliation: Departamento de Física, Universidade Estadual de Ponta Grossa, Avenida Carlos Cavalcanti 4748, 84030-900 Ponta Grossa-PR, Brazil.|National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil.
authors.forename: E K
authors.initials: EK
authors.lastname: Lenzi
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil.|National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil.
authors.forename: F D
authors.initials: FD
authors.lastname: Nobre