Entropy Production in a Fractal System with Diffusive Dynamics

Rafael S Zola; Ervin K Lenzi; Luciano R da Silva; Marcelo K Lenzi

doi:10.3390/e25121578

Entropy Production in a Fractal System with Diffusive Dynamics

Entropy (Basel). 2023 Nov 23;25(12):1578. doi: 10.3390/e25121578.

Authors

Rafael S Zola¹, Ervin K Lenzi², Luciano R da Silva³, Marcelo K Lenzi⁴

Affiliations

¹ Departmento de Física, Universidade Tecnológica Federal do Paraná-Campus de Apucarana, Apucarana 86812-460, PR, Brazil.
² Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil.
³ Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil.
⁴ Departamento de Engenharia Química, Universidade Federal do Paraná, Curitiba 81531-980, PR, Brazil.

Abstract

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.

Keywords: H-theorem; entropy production; generalized entropies; nonlinear diffusion.

Grants and funding

E.K.L. thanks partial financial support of the CNPq under Grant No. 301715/2022-0. R.S.Z. thanks the National Council for Scientific and Technological Development, CNPq, process number 304634/2020-4 and 465259/2014-6, the National Institute of Science and Technology Complex Fluids (INCT-FCx), and the São Paulo Research Foundation (FAPESP–2014/50983-3).