Nonlinear Kramers equation associated with nonextensive statistical mechanics

被引：25

作者：

Mendes, G. A. ^{[1
]}

Ribeiro, M. S. ^{[2
]}

Mendes, R. S. ^{[3
,5
]}

Lenzi, E. K. ^{[4
,5
]}

Nobre, F. D. ^{[2
,5
]}

机构：

[1] Univ Fed Maranhao, Dept Fis, BR-65080805 Sao Luis, MA, Brazil

[2] Ctr Brasileiro Pesquisas Fis, BR-22290180 Rio De Janeiro, RJ, Brazil

[3] Univ Estadual Maringa, Dept Fis, BR-8702090 Maringa, PR, Brazil

[4] Univ Estadual Ponta Grossa, Dept Fis, BR-84030900 Ponta Grossa, PR, Brazil

[5] Natl Inst Sci & Technol Complex Syst, BR-22290180 Rio De Janeiro, RJ, Brazil

来源：

PHYSICAL REVIEW E | 2015年 / 91卷 / 05期

关键词：

FOKKER-PLANCK EQUATIONS; ANOMALOUS DIFFUSION; GENERALIZED ENTROPIES; H-THEOREM; BOLTZMANN; DYNAMICS;

D O I：

10.1103/PhysRevE.91.052106

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

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.

引用

页数：8

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