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Entropy
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Ring, Phases, Self-Similarity, Disorder, Entropy, Information
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Ring, Phases, Self-Similarity, Disorder, Entropy, Information

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

Deadline for manuscript submissions: closed (30 September 2020) | Viewed by 5331

Special Issue Editors

Prof. Alain Le Méhauté

E-Mail
Guest Editor
1. Materials Design SARL, 18, Rue Saisset 91 120 Montrouge, France
2. Kazan Federal University, 18-35 Kremlyovskaya Ulica, 42 0008 Kazan, Russia
Interests: nonlinear dynamics; non-integer differential equations and applications (electrodynamics and mechanics); molecular simulation of materials; number theory; category theory; management of creativity
Dr. Alina Cristiana Gavriluţ

E-Mail Website
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

Special Issue Information

Dear Colleaues,

Information and Entropy are challenging notions for theoretical modeling, technical analysis and numerical simulation, in physics and mathematics. In fact, information and entropy lead the closing of complex systems. In this frame, the concept of the interior and exterior involves the fundamental issues of self-referencing. In particular, we can observe that many developments in mathematics are currently based on self-referencing, the fractality of which gives a geometric image. We can find this self-reference included in arithmetic (e.g., Conway's Surreal) and obviously in computer science. In this context, the notions of time play a key role as shown in computation, and consequently the notions of entropy, namely of energy dissipation, associated with them. Category theory opens up new perspectives in this issue because the notion of adjunction builds the self-reference (possibly filtered), which then appears to be consubstantial with this theory, which, being linked to the concept of physical action, creates a link between the concept of morphism and information, and therefore between information and irreversible processes (procedures). Theories and applications developed based on these fundamental concepts, and other related ones, are considered a veritable contribution to this Special Issue.

Potential topics include, but are not limited to, the following:

  • Towards explicit information through operational procedures;
  • Applications of the operational procedures in order to extract information and to highlight its role in the phenomena dynamics;
  • Differentiability and non-differentiability in complex systems through parameters-scales dependence; Implications in information theory;
  • Ambiguity of quantum information and stochastic related notions in the context of (multi)fractal theories; Scaling properties and chance;
  • Fractional derivatives models in complex systems dynamics, lattices, information distribution (and which support information), symmetry breaking;
  • Toward the different concepts of time;
  • Complexity through modular arithmetic and fibering;
  • The maximal informational energy in the sense of Onicescu, as a fundamental part of the implicit–explicit information transition;
  • Elements of (multifractal) additive/non-additive measure theory with implications in the complex capacitive systems dynamics;
  • Space-time holographic theories, phase and role of the informational energy in such context.

Original papers relating to a certain objective are especially welcome.

We hope to attract review articles which describe the current state of the art in these areas.

Prof. Alain Le Méhauté
Prof. Alina Cristiana Gavriluţ
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

  • self reference
  • modular frames
  • non-additivity
  • fractality
  • uncertainty
  • times
  • quantum mechanics
  • open systems
  • brain
  • computation complexity
  • entropy

Published Papers (3 papers)

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Research

20 pages, 3954 KiB  
Article
Multifractality through Non-Markovian Stochastic Processes in the Scale Relativity Theory. Acute Arterial Occlusions as Scale Transitions
by Nicolae Dan Tesloianu, Lucian Dobreci, Vlad Ghizdovat, Andrei Zala, Adrian Valentin Cotirlet, Alina Gavrilut, Maricel Agop, Decebal Vasincu, Igor Nedelciuc, Cristina Marcela Rusu and Irina Iuliana Costache
Entropy 2021, 23(4), 444; https://doi.org/10.3390/e23040444 - 9 Apr 2021
Viewed by 1556
Abstract
By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale’s sense and/or the form of the multifractal theory of motion). [...] Read more.
By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale’s sense and/or the form of the multifractal theory of motion). By operating in the context of the multifractal theory of motion, based on multifractalization through non-Markovian stochastic processes, the main results of Nottale’s theory can be generalized (specific momentum conservation laws, both at differentiable and non-differentiable resolution scales, specific momentum conservation law associated with the differentiable–non-differentiable scale transition, etc.). In such a context, all results are explicated through analyzing biological processes, such as acute arterial occlusions as scale transitions. Thus, we show through a biophysical multifractal model that the blocking of the lumen of a healthy artery can happen as a result of the “stopping effect” associated with the differentiable-non-differentiable scale transition. We consider that blood entities move on continuous but non-differentiable (multifractal) curves. We determine the biophysical parameters that characterize the blood flow as a Bingham-type rheological fluid through a normal arterial structure assimilated with a horizontal “pipe” with circular symmetry. Our model has been validated based on experimental clinical data. Full article
(This article belongs to the Special Issue Ring, Phases, Self-Similarity, Disorder, Entropy, Information)
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16 pages, 2593 KiB  
Article
The Role of Information in Managing Interactions from a Multifractal Perspective
by Maricel Agop, Stefan Andrei Irimiciuc, Adrian Ghenadi, Luminita Bibire, Stefan Toma, Tudor-Cristian Petrescu, Dorin Vaideanu, Cristina Marcela Rusu, Alina Gavrilut and Decebal Vasincu
Entropy 2021, 23(2), 148; https://doi.org/10.3390/e23020148 - 26 Jan 2021
Viewed by 1445
Abstract
In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various [...] Read more.
In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”. Full article
(This article belongs to the Special Issue Ring, Phases, Self-Similarity, Disorder, Entropy, Information)
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17 pages, 7913 KiB  
Article
Toward Interactions through Information in a Multifractal Paradigm
by Maricel Agop, Alina Gavriluț, Claudia Grigoraș-Ichim, Ștefan Toma, Tudor-Cristian Petrescu and Ștefan Andrei Irimiciuc
Entropy 2020, 22(9), 987; https://doi.org/10.3390/e22090987 - 4 Sep 2020
Cited by 2 | Viewed by 1888
Abstract
In a multifractal paradigm of motion, Shannon’s information functionality of a minimization principle induces multifractal–type Newtonian behaviors. The analysis of these behaviors through motion geodesics shows the fact that the center of the Newtonian-type multifractal force is different from the center of the [...] Read more.
In a multifractal paradigm of motion, Shannon’s information functionality of a minimization principle induces multifractal–type Newtonian behaviors. The analysis of these behaviors through motion geodesics shows the fact that the center of the Newtonian-type multifractal force is different from the center of the multifractal trajectory. The measure of this difference is given by the eccentricity, which depends on the initial conditions. In such a context, the eccentricities’ geometry becomes, through the Cayley–Klein metric principle, the Lobachevsky plane geometry. Then, harmonic mappings between the usual space and the Lobachevsky plane in a Poincaré metric can become operational, a situation in which the Ernst potential of general relativity acquires a classical nature. Moreover, the Newtonian-type multifractal dynamics, perceived and described in a multifractal paradigm of motion, becomes a local manifestation of the gravitational field of general relativity. Full article
(This article belongs to the Special Issue Ring, Phases, Self-Similarity, Disorder, Entropy, Information)
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