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Entropy
Volume 26
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10.3390/e26080673
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Article

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

by
Ervin K. Lenzi
1,2,*,
Michely P. Rosseto
1,
Derik W. Gryczak
3,
Luiz R. Evangelista
4,5,6,
Luciano R. da Silva
2,7,
Marcelo K. Lenzi
8 and
Rafael S. Zola
9
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
*
Author to whom correspondence should be addressed.
Entropy 2024, 26(8), 673; https://doi.org/10.3390/e26080673
Submission received: 9 July 2024 / Revised: 4 August 2024 / Accepted: 7 August 2024 / Published: 8 August 2024
(This article belongs to the Special Issue Theory and Applications of Hyperbolic Diffusion and Shannon Entropy)
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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.
Keywords: entropy; nonlinear diffusion; anomalous diffusion; H-theorem entropy; nonlinear diffusion; anomalous diffusion; H-theorem

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MDPI and ACS Style

Lenzi, E.K.; Rosseto, M.P.; Gryczak, D.W.; Evangelista, L.R.; da Silva, L.R.; Lenzi, M.K.; Zola, R.S. Generalized Kinetic Equations with Fractional Time-Derivative and Nonlinear Diffusion: H-Theorem and Entropy. Entropy 2024, 26, 673. https://doi.org/10.3390/e26080673

AMA Style

Lenzi EK, Rosseto MP, Gryczak DW, Evangelista LR, da Silva LR, Lenzi MK, Zola RS. Generalized Kinetic Equations with Fractional Time-Derivative and Nonlinear Diffusion: H-Theorem and Entropy. Entropy. 2024; 26(8):673. https://doi.org/10.3390/e26080673

Chicago/Turabian Style

Lenzi, Ervin K., Michely P. Rosseto, Derik W. Gryczak, Luiz R. Evangelista, Luciano R. da Silva, Marcelo K. Lenzi, and Rafael S. Zola. 2024. "Generalized Kinetic Equations with Fractional Time-Derivative and Nonlinear Diffusion: H-Theorem and Entropy" Entropy 26, no. 8: 673. https://doi.org/10.3390/e26080673

APA Style

Lenzi, E. K., Rosseto, M. P., Gryczak, D. W., Evangelista, L. R., da Silva, L. R., Lenzi, M. K., & Zola, R. S. (2024). Generalized Kinetic Equations with Fractional Time-Derivative and Nonlinear Diffusion: H-Theorem and Entropy. Entropy, 26(8), 673. https://doi.org/10.3390/e26080673

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