Schwämmle Veit, Nobre Fernando D, Curado Evaldo M F
Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Oct;76(4 Pt 1):041123. doi: 10.1103/PhysRevE.76.041123. Epub 2007 Oct 17.
A general type of nonlinear Fokker-Planck equation is derived directly from a master equation, by introducing generalized transition rates. The H theorem is demonstrated for systems that follow those classes of nonlinear Fokker-Planck equations, in the presence of an external potential. For that, a relation involving terms of Fokker-Planck equations and general entropic forms is proposed. It is shown that, at equilibrium, this relation is equivalent to the maximum-entropy principle. Families of Fokker-Planck equations may be related to a single type of entropy, and so, the correspondence between well-known entropic forms and their associated Fokker-Planck equations is explored. It is shown that the Boltzmann-Gibbs entropy, apart from its connection with the standard--linear Fokker-Planck equation--may be also related to a family of nonlinear Fokker-Planck equations.
通过引入广义跃迁速率，直接从主方程导出了一种一般类型的非线性福克 - 普朗克方程。对于遵循这些类别的非线性福克 - 普朗克方程的系统，在存在外部势的情况下证明了H定理。为此，提出了一个涉及福克 - 普朗克方程项和一般熵形式的关系式。结果表明，在平衡时，该关系式等同于最大熵原理。福克 - 普朗克方程族可能与单一类型的熵相关，因此，探索了著名的熵形式与其相关的福克 - 普朗克方程之间的对应关系。结果表明，玻尔兹曼 - 吉布斯熵，除了与标准线性福克 - 普朗克方程的联系之外，还可能与一族非线性福克 - 普朗克方程相关。
