Maximum Path Information and Fokker-Planck Equation

我们在场从 Maupertuis 的最少的行动的原则的归纳直接导出异常散开的非线性的佛克普朗克常数(FP ) 方程的一个严密方法由王求婚了[混乱， Solitons 和分数维图形 23 (2005 ) 1253 ] 为在 Markovian 演变的光滑或伪光滑的不规则的动力学过程。获得的 FP 方程可以拿二种不同却相等的形式。散开常数可以取决于两 q，这也被发现(Tsallis 熵的索引[J。Stat。Phys。52 (1988 ) 479 ] 并且时间 t ) 。

We present a rigorous method to derive the nonlinear Fokker-Planck （FP） equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons ＆ Fractals 23 （2005） 1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q （the index of Tsallis entropy [J. Stat. Phys. 52 （1988） 479] and the time t.