Curl Forces and the Nonlinear Fokker-Planck Equation
Abstract
Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are -exponentials of an appropriate potential function, are determined. It is proved that when these stationary solutions exist, the nonlinear Fokker-Planck equations satisfy an -theorem in terms of a free-energy like quantity involving the entropy. A particular two dimensional model admitting analytical, time-dependent, -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.
Cite
@article{arxiv.1609.00972,
title = {Curl Forces and the Nonlinear Fokker-Planck Equation},
author = {R. S. Wedemann and A. R. Plastino and C. Tsallis},
journal= {arXiv preprint arXiv:1609.00972},
year = {2016}
}