Generalized Kinetic Equations with Fractional Time-Derivative and Nonlinear Diffusion: H-Theorem and Entropy-Reference-Cited by-同舟云学术

Generalized Kinetic Equations with Fractional Time-Derivative and Nonlinear Diffusion: H-Theorem and Entropy

Published:2024-08-08 Issue:8 Volume:26 Page:673
ISSN:1099-4300
Container-title:Entropy
language:en
Short-container-title:Entropy

Author:

Lenzi Ervin K.¹²^ORCID,Rosseto Michely P.¹^ORCID,Gryczak Derik W.³^ORCID,Evangelista Luiz R.⁴⁵⁶^ORCID,da Silva Luciano R.²⁷^ORCID,Lenzi Marcelo K.⁸^ORCID,Zola Rafael S.⁹^ORCID

Affiliation:

1. Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil

2. National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro 22290-180, RJ, Brazil

3. Independent Researcher, Irati 84507-012, PR, Brazil

4. Departamento de Física, Universidade Estadual de Maringá, Maringá 87020-900, PR, Brazil

5. Istituto dei Sistemi Complessi (ISC–CNR), Via dei Taurini, 19, 00185 Rome, Italy

6. Department of Molecular Science and Nanosystems, Ca’Foscari University of Venice, Via Torino, 155, 30172 Mestre, Italy

7. Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil

8. Departamento de Engenharia Química, Universidade Federal do Paraná, Curitiba 80060-000, PR, Brazil

9. Department of Physics, Universidade Tecnológica Federal do Paraná, Apucarana 86812-460, PR, Brazil

Abstract

We investigate the H-theorem for a class of generalized kinetic equations with fractional time-derivative, hyperbolic term, and nonlinear diffusion. When the H-theorem is satisfied, we demonstrate that different entropic forms may emerge due to the equation’s nonlinearity. We obtain the entropy production related to these entropies and show that its form remains invariant. Furthermore, we investigate some behaviors for these equations from both numerical and analytical perspectives, showing a large class of behaviors connected with anomalous diffusion and their effects on entropy.

Funder

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Program of Visiting Professor of Universtità Ca’ Foscari of Venice

CNPq

National Council for Scientific and Technological Development, CNPq

National Institute of Science and Technology Complex Fluids

São Paulo Research Foundation

National Institute of Science and Technology of Complex Systems

Publisher

MDPI AG

Link

https://www.mdpi.com/1099-4300/26/8/673/pdf

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