摘要翻译：
最近引入的非线性Fokker-Planck方程是直接从主方程导出的，它是一个非常通用的工具，用来描述在外力存在下呈现复杂行为的唯象系统，如反常扩散。这样一个方程的特征是一个非线性扩散项，一般而言，它可能呈现概率分布的两个不同的幂。在此，我们计算了该方程在某些特殊情况下的定态分布，并引入了相应的广义熵类以满足H-定理。在这种方法中，与原始主方程的跃迁速率相关的参数与这种广义熵有关，并被证明服从一些限制。讨论了一些特殊情况。
---
英文标题：
《A General Nonlinear Fokker-Planck Equation and its Associated Entropy》
---
作者：
Veit Schwammle, Evaldo M. F. Curado, Fernando D. Nobre
---
最新提交年份：
2007
---
分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--
一级分类：Physics        物理学
二级分类：Other Condensed Matter        其他凝聚态物质
分类描述：Work in condensed matter that does not fit into the other cond-mat classifications
在不适合其他cond-mat分类的凝聚态物质中工作
--

---
英文摘要：
  A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence of external forces. Such an equation is characterized by a nonlinear diffusion term that may present, in general, two distinct powers of the probability distribution. Herein, we calculate the stationary-state distributions of this equation in some special cases, and introduce associated classes of generalized entropies in order to satisfy the H-theorem. Within this approach, the parameters associated with the transition rates of the original master-equation are related to such generalized entropies, and are shown to obey some restrictions. Some particular cases are discussed.
---
PDF链接：
https://arxiv.org/pdf/704.0465