Wedemann R S, Plastino A R, Tsallis C
Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-900 Rio de Janeiro, Rio de Janeiro, Brazil.
CeBio y Secretaría de Investigación, Universidad Nacional del Noroeste de la Província de Buenos Aires, UNNOBA, CONICET, Roque Saenz Peña 456, Junín, 2700 Buenos Aires, Argentina.
Phys Rev E. 2016 Dec;94(6-1):062105. doi: 10.1103/PhysRevE.94.062105. Epub 2016 Dec 2.
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.
研究了具有旋度漂移力的非线性福克 - 普朗克方程。确定了这些演化方程允许存在平稳解的条件，这些平稳解是适当势函数的q指数形式。证明了当这些平稳解存在时，非线性福克 - 普朗克方程就一个涉及(S_{q})熵的类似自由能的量而言满足一个H定理。详细讨论了一个允许解析的、与时间有关的q - 高斯解的二维模型。该模型描述了一个具有短程相互作用的粒子系统，在旋转阻力介质引起的拖曳效应下进行过阻尼运动。它与最近应用于第二类超导体研究的模型有关。讨论了当前进展与物理、天文学和生物学中复杂系统研究的相关性。
