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Entropy
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Theory and Applications of Hyperbolic Diffusion and Shannon Entropy
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Theory and Applications of Hyperbolic Diffusion and Shannon Entropy

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: 15 January 2025 | Viewed by 3048

Special Issue Editor

Prof. Dr. Manuel O. Cáceres

E-Mail Website
Guest Editor
Comisión Nacional de Energía Atómica (CNEA), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Centro Atómico Bariloche and Instituto Balseiro, Universidad Nacional de Cuyo, Av. E. Bustillo 9500, Bariloche CP8400, Argentina
Interests: stochastic processes; disorder; non-equilibrium statistical mechanics; quantum open system

Special Issue Information

Dear Colleagues,

Diffusion is ubiquitous in science, while a model of instantaneous propagation for the process itself is a matter of discussion in the real natural world. Examples of finite-velocity diffusion are heat waves in simple and complex materials, transport in special relativity, biological space-dependent population models, competition, and coupled systems in ecological transport, run-and-tumble biological motion, the geophysical earth's climate problems, neuroscience and its transport electric brain behavior, and transport in electronic circuits and in guide waves, as well as in the socio-economic propagation of information models.

The use of the canonical Fick law to study the behavior of such a system has acquired significant importance in the pioneer works of transport theory, while the Cattaneo–Fick’s law is focused on considering the finite-velocity diffusion propagation. In a related context, the telegrapher’s equation—in the wave propagation approach—addresses the important interest of describing electromagnetic transport in conducting media from a theoretical and/or experimental viewpoint. Additionally, surface gravitational waves on random media are describes by the telegrapher’s equation.

The application of information theory to study these diffusion-like systems is an open statistics problem. Further progress on this matter calls for new statistical techniques based on the Shannon entropy theory, as well as for an improved understanding of the hyperbolic diffusion problem and the waves in the stochastic telegrapher’s equation for complex systems. Contributions addressing any of these issues are very welcome.

This Special Issue aims to be a forum for the presentation of improved techniques for these kinds of finite-velocity diffusion-like systems. The analysis and interpretation of the hyperbolic diffusion using statistical tools based on the Shannon information theory fall within the scope of this Special Issue.

Prof. Dr. Manuel O. Cáceres
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • finite-velocity diffusion
  • wave telegrapher’s equation
  • stochastic and random media
  • statistics information theory
  • complex transport
  • random waves and dispersion
  • physics
  • chemistry
  • biology
  • earth sciences
  • social sciences

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Published Papers (3 papers)

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Research

18 pages, 4026 KiB  
Article
Generalized Kinetic Equations with Fractional Time-Derivative and Nonlinear Diffusion: H-Theorem and Entropy
by Ervin K. Lenzi, Michely P. Rosseto, Derik W. Gryczak, Luiz R. Evangelista, Luciano R. da Silva, Marcelo K. Lenzi and Rafael S. Zola
Entropy 2024, 26(8), 673; https://doi.org/10.3390/e26080673 - 8 Aug 2024
Viewed by 682
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Theory and Applications of Hyperbolic Diffusion and Shannon Entropy)
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19 pages, 2444 KiB  
Article
Fractional Telegrapher’s Equation under Resetting: Non-Equilibrium Stationary States and First-Passage Times
by Katarzyna Górska, Francisco J. Sevilla, Guillermo Chacón-Acosta and Trifce Sandev
Entropy 2024, 26(8), 665; https://doi.org/10.3390/e26080665 - 5 Aug 2024
Viewed by 678
Abstract
We consider two different time fractional telegrapher’s equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates [...] Read more.
We consider two different time fractional telegrapher’s equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates due to the resetting mechanism. We also obtain the fractional telegraph process as a subordinated telegraph process by introducing operational time such that the physical time is considered as a Lévy stable process whose characteristic function is the Lévy stable distribution. We also analyzed the survival probability for the first-passage time problem and found the optimal resetting rate for which the corresponding mean first-passage time is minimal. Full article
(This article belongs to the Special Issue Theory and Applications of Hyperbolic Diffusion and Shannon Entropy)
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16 pages, 413 KiB  
Article
Fisher and Shannon Functionals for Hyperbolic Diffusion
by Manuel O. Cáceres, Marco Nizama and Flavia Pennini
Entropy 2023, 25(12), 1627; https://doi.org/10.3390/e25121627 - 6 Dec 2023
Cited by 2 | Viewed by 1091
Abstract
The complexity measure for the distribution in space-time of a finite-velocity diffusion process is calculated. Numerical results are presented for the calculation of Fisher’s information, Shannon’s entropy, and the Cramér–Rao inequality, all of which are associated with a positively normalized solution to the [...] Read more.
The complexity measure for the distribution in space-time of a finite-velocity diffusion process is calculated. Numerical results are presented for the calculation of Fisher’s information, Shannon’s entropy, and the Cramér–Rao inequality, all of which are associated with a positively normalized solution to the telegrapher’s equation. In the framework of hyperbolic diffusion, the non-local Fisher’s information with the x-parameter is related to the local Fisher’s information with the t-parameter. A perturbation theory is presented to calculate Shannon’s entropy of the telegrapher’s equation at long times, as well as a toy model to describe the system as an attenuated wave in the ballistic regime (short times). Full article
(This article belongs to the Special Issue Theory and Applications of Hyperbolic Diffusion and Shannon Entropy)
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