Curl Forces and the Nonlinear Fokker-Planck Equation

Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are \(q\)-exponentials of an appropriate potential function, are determined. It is proved that when these stationary solutions exi...

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Bibliographic Details
Published in:arXiv.org 2016-09
Main Authors: Wedemann, R S, Plastino, A R, Tsallis, C
Format: Article
Language:English
Subjects:
Astronomy
Complex systems
Fokker-Planck equation
Nonlinear equations
Time dependence
Two dimensional analysis
Two dimensional models
Online Access:Get full text
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Summary:Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are \(q\)-exponentials of an appropriate potential function, are determined. It is proved that when these stationary solutions exist, the nonlinear Fokker-Planck equations satisfy an \(H\)-theorem in terms of a free-energy like quantity involving the \(S_q\) entropy. A particular two dimensional model admitting analytical, time-dependent, \(q\)-Gaussian solutions is discussed in detail. This model describes a system of particles with short-range interactions, performing overdamped motion under drag effects, due to a rotating resisting medium. It is related to models that have been recently applied to the study of type-II superconductors. The relevance of the present developments to the study of complex systems in physics, astronomy, and biology, is discussed.
ISSN:2331-8422
DOI:10.48550/arxiv.1609.00972