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Entropy
Special Issues
Multifractality and Information Theories: Fundaments and Applications
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Multifractality and Information Theories: Fundaments and Applications

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

Deadline for manuscript submissions: closed (20 January 2022) | Viewed by 1791

Special Issue Editors

Dr. Alina Cristiana Gavriluţ

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Guest Editor
Department of Mathematics, “Al. I. Cuza” University of Iasi, 700506 Iasi, Romania
Interests: set-valued measures; non-additive measures; set-valued integrals; non-additive integrals; topology; fractals; multifractals; nonlinear dynamics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Maricel Agop

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Guest Editor
Department of Physics, Faculty of Machine Manufacturing and Industrial Management, “Gheorghe Asachi” Technical University of Iasi, 700050 Iasi, Romania
Interests: fractal theory; nonlinear dynamics; quantum mechanics; fields theory; neuroscience
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Relations among standard information theories and multifractal theories of the motion are intended to be established in this Special Issue (cosmological theories, grand unification theories, scale relativity theories, fractional derivative theories, classical information theory, quantum information theory, fractal information theories, etc.), with special considerations concerning dynamics in biological structures. Different types of information (Fisher, Shannon, etc.) and their correlations with entropy, based on operational procedures, are also expected (group invariances, differential geometries of Riemann type, spatial–temporal compactifications of dimensions, embeddings, etc.).

Dr. Alina Cristiana Gavriluţ
Prof. Dr. Maricel Agop
Guest Editors

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

  • information
  • fractal theory
  • measure theory
  • quantum measure theory
  • topology
  • fractional derivative theory
  • quantum physics
  • cosmology
  • fractal cosmology
  • fractal mechanics

Published Papers (1 paper)

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Research

23 pages, 8506 KiB  
Article
Implications and Consequences of SL(2R) as Invariance Group in the Description of Complex Systems Dynamics from a Multifractal Perspective of Motion
by Lucian Dobreci, Oana Rusu, Decebal Vasincu, Mihaela Jarcău, Cristina Marcela Rusu, Silviu Gurlui, Vlad Ghizdovat, Alina Gavrilut and Maricel Agop
Entropy 2022, 24(4), 484; https://0-doi-org.brum.beds.ac.uk/10.3390/e24040484 - 30 Mar 2022
Viewed by 1212
Abstract
Possible implications and consequences of using SL(2R) as invariance groups in the description at any scale resolution of the dynamics of any complex system are analyzed. From this perspective and based on Jaynes’ remark (any circumstance left unspecified in the description of any [...] Read more.
Possible implications and consequences of using SL(2R) as invariance groups in the description at any scale resolution of the dynamics of any complex system are analyzed. From this perspective and based on Jaynes’ remark (any circumstance left unspecified in the description of any complex system dynamics has the concrete expression in the existence of an invariance group), in the present paper one specifies such unspecified circumstances that result directly from the consideration of the canonical formalism induced by the SL(2R) as invariance group. It follows that both the Hamiltonian function and the Guassian distribution acquire the status of invariant group functions, the parameters that define the Hamiltonian acquire statistical significances based on a principle of maximizing informational energy, the class of statistical hypotheses specific to Gaussians of the same average acts as transitivity manifolds of the group (transitivity manifolds which can be correlated with the multifractal-non-multifractal scale transitions), joint invariant functions induced through SL(2R) groups isomorphism (the SL(2R) variables group, and the SL(2R) parameters group, etc.). For an ensemble of oscillators of the same frequency, the unspecified circumstances return to the ignorance of the amplitude and phase of each of the oscillators, which forces the recourse to a statistical ensemble traversed by the transformations of the Barbilian-type group. Finally, the model is validated based on numerical simulations and experimental results that refer to transient phenomena in ablation plasmas. The novelty of our model resides in the fact that fractalization through stochasticization is imposed through group invariance, situation in which the group’s transitivity manifolds can be correlated with the scale resolution. Full article
(This article belongs to the Special Issue Multifractality and Information Theories: Fundaments and Applications)
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