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Agop M, Irimiciuc SA, Ghenadi A, Bibire L, Toma S, Petrescu TC, Vaideanu D, Rusu CM, Gavrilut A, Vasincu D. The Role of Information in Managing Interactions from a Multifractal Perspective. ENTROPY 2021; 23:e23020148. [PMID: 33530405 PMCID: PMC7911553 DOI: 10.3390/e23020148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/30/2020] [Revised: 01/21/2021] [Accepted: 01/22/2021] [Indexed: 11/16/2022]
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 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”.
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Affiliation(s)
- Maricel Agop
- Department of Physics, Gh. Asachi Technical University of Iași, 700050 Iași, Romania; (M.A.); (C.M.R.)
- Romanian Scientists Academy, 54 Splaiul Independentei, 050094 Bucharest, Romania
| | - Stefan Andrei Irimiciuc
- National Institute for Laser, Plasma and Radiation Physics, 409 Atomistilor Street, 077125 Bucharest, Romania;
| | - Adrian Ghenadi
- Department of Industrial Systems Engineering and Management, Faculty of Engineering, University of Bacau, Calea Mărășești 157, 600115 Bacau, Romania;
| | - Luminita Bibire
- Department of Environmental Engineering and Mechanical Engineering, Faculty of Engineering, University of Bacau, Calea Mărășești 157, 600115 Bacau, Romania;
| | - Stefan Toma
- Department of Material Engineering and Industrial Security, Gh. Asachi Technical University of Iași, 700050 Iași, Romania;
| | - Tudor-Cristian Petrescu
- Department of Structural Mechanics, Gh. Asachi Technical University of Iași, 700050 Iași, Romania;
| | - Dorin Vaideanu
- Physics Faculty, Alexandru Ioan Cuza University of Iași, 700050 Iași, Romania;
| | - Cristina Marcela Rusu
- Department of Physics, Gh. Asachi Technical University of Iași, 700050 Iași, Romania; (M.A.); (C.M.R.)
| | - Alina Gavrilut
- Mathematics Faculty, Alexandru Ioan Cuza University of Iași, 700050 Iași, Romania
- Correspondence:
| | - Decebal Vasincu
- University of Medicine and Farmacy Grigore T. Popa Iași, 700050 Iași, Romania;
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Agop M, Gavriluț A, Grigoraș-Ichim C, Toma Ș, Petrescu TC, Irimiciuc ȘA. Toward Interactions through Information in a Multifractal Paradigm. ENTROPY (BASEL, SWITZERLAND) 2020; 22:e22090987. [PMID: 33286755 PMCID: PMC7597305 DOI: 10.3390/e22090987] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Revised: 08/11/2020] [Accepted: 09/01/2020] [Indexed: 06/12/2023]
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 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.
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Affiliation(s)
- Maricel Agop
- Department of Physics, “Gh. Asachi” Technical University of Iasi, 700050 Iasi, Romania;
- Romanian Scientists Academy, 54 Splaiul Independentei, 050094 Bucharest, Romania
| | - Alina Gavriluț
- Department of Mathematics, “Al. I. Cuza” University of Iasi, 700506 Iasi, Romania
| | - Claudia Grigoraș-Ichim
- Department of Accounting, Audit and Financing, “Stefan cel Mare” University of Suceava, 720229 Suceava, Romania;
| | - Ștefan Toma
- Department of Material Engineering and Industrial Security, “Gh. Asachi” Technical University of Iasi, 700050 Iasi, Romania;
| | - Tudor-Cristian Petrescu
- Department of Structural Mechanics, “Gh. Asachi” Technical University of Iasi, 700050 Iasi, Romania;
| | - Ștefan Andrei Irimiciuc
- National Institute for Laser, Plasma and Radiation Physics, 409 Atomistilor Street, 077125 Bucharest, Romania;
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