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摘要翻译：
通过引入广义跃迁率，直接从主方程导出了一般类型的非线性Fokker-Planck方程。证明了在外势存在下，遵循这类非线性Fokker-Planck方程的系统的H定理。为此，提出了一个包含Fokker-Planck方程项和一般熵形式的关系式。结果表明，在平衡状态下，这种关系等价于最大熵原理。Fokker-Planck方程族可能与单一类型的熵有关，因此，本文探讨了著名的熵形式与其相关的Fokker-Planck方程之间的对应关系。结果表明，Boltzmann-Gibbs熵除与标准的线性Fokker-Planck方程有关外，还可能与一类非线性Fokker-Planck方程有关。
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英文标题：
《Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations》
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作者：
Veit Schwammle, Fernando D. Nobre and Evaldo M. F. Curado
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最新提交年份：
2007
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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
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/707.3153
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