Zola Rafael S, Lenzi Ervin K, da Silva Luciano R, Lenzi Marcelo K
Departmento de Física, Universidade Tecnológica Federal do Paraná-Campus de Apucarana, Apucarana 86812-460, PR, Brazil.
Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil.
Entropy (Basel). 2023 Nov 23;25(12):1578. doi: 10.3390/e25121578.
We study the entropy production in a fractal system composed of two subsystems, each of which is subjected to an external force. This is achieved by using the H-theorem on the nonlinear Fokker-Planck equations (NFEs) characterizing the diffusing dynamics of each subsystem. In particular, we write a general NFE in terms of Hausdorff derivatives to take into account the metric of each system. We have also investigated some solutions from the analytical and numerical point of view. We demonstrate that each subsystem affects the total entropy and how the diffusive process is anomalous when the fractal nature of the system is considered.
我们研究了一个由两个子系统组成的分形系统中的熵产生，每个子系统都受到一个外力作用。这是通过对表征每个子系统扩散动力学的非线性福克 - 普朗克方程（NFEs）使用H定理来实现的。特别地，我们根据豪斯多夫导数写出一个通用的NFE，以考虑每个系统的度量。我们还从解析和数值的角度研究了一些解。我们证明了每个子系统如何影响总熵，以及当考虑系统的分形性质时扩散过程是如何反常的。
