Generalization of the variational formulation of the Onsager–Machlup thermodynamic theory of fluctuation is considered. Within the framework of variational theory, we introduce the time-dependent generalized normal distribution and Hamilton–Jacobi equation. The family of higher-order partial differential equations, which generalize classical Fokker–Planck equation, is considered. It is shown that proposed theory can be used for describing anomalous diffusion.

中文翻译：

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Onsager-Machlup 波动理论和随时间变化的广义正态分布

考虑了 Onsager-Machlup 热力学涨落理论的变分公式的推广。在变分理论的框架内，我们介绍了时间相关的广义正态分布和 Hamilton-Jacobi 方程。考虑了推广经典 Fokker–Planck 方程的高阶偏微分方程族。结果表明，所提出的理论可用于描述反常扩散。