Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.7
2.7
Journals
Entropy
Special Issues
New Trends in Theoretical and Mathematical Physics
entropy-logo
Submit to Entropy Review for Entropy Propose a Special Issue

Journal Menu

► Journal Menu

Journal Browser

► Journal Browser
share announcement

New Trends in Theoretical and Mathematical Physics

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

Deadline for manuscript submissions: closed (8 December 2023) | Viewed by 6806

Special Issue Editors

Prof. Dr. Wilson A. Zuniga-Galindo

E-Mail Website
Guest Editor
School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX 78539, USA
Interests: mathematical physics; differential equations on networks; ultrametricity in physics; complex systems; p-adic analysis; probability in ultrametric spaces; algebraic geometry
Prof. Dr. Jing Li

E-Mail Website
Guest Editor
Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China
Interests: mathematical physics; differential equations and dynamical systems; nonlinear dynamics; vibration and control; nonlinear dynamic absorber
Prof. Dr. Hugo García-Compeán

E-Mail Website
Guest Editor
Center for Research and Advanced Studies of the National Polytechnic Institute, Mexico City 07360, Mexico
Interests: quantum field theory; general relativity; M-theory; theoretical high energy physics

Special Issue Information

Dear Colleagues,

The Special Issue on “New Trends in Theoretical and Mathematical Physics” aims to be a forum for the presentation of new, highly interdisciplinary, and actively developing branches of mathematical and theoretical physics. We mention, by way of example, that the interactions between artificial intelligence and high-energy physics are an important research frontier. These interactions range from using machine learning to analyzing experimental data in high-energy physics, to the conjecture that a correspondence exists between neural networks and Euclidean quantum field theories that might further the understanding of deep learning architectures.

This Special Issue will accept unpublished original papers and comprehensive reviews focused on, but not limited to, the following research areas:

  • Neural networks, quantum field theories, and quantum information;
  • Tensor networks and their applications;
  • Mathematical structures emerging in quantum theories;
  • Complex systems and networks;
  • p-adic mathematical physics;
  • Open quantum systems and quantum thermodynamics;
  • Differential equations, symmetries, Hamiltonian structures, Conservation laws, infinite dimensional algebras, and their applications in high-energy physics and related areas.

Prof. Dr. Wilson A. Zuniga-Galindo
Prof. Dr. Jing Li
Prof. Dr. Hugo García-Compeán
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

  • artificial intelligence
  • theoretical physics
  • mathematical models
  • complex systems
  • symmetries
  • Hamiltonian structures

Published Papers (6 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

25 pages, 12596 KiB  
Article
H∞ Optimization of Three-Element-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Based on the Particle Swarm Algorithm
by Ting Gao, Jing Li, Shaotao Zhu, Xiaodong Yang and Hongzhen Zhao
Entropy 2023, 25(7), 1048; https://doi.org/10.3390/e25071048 - 12 Jul 2023
Cited by 3 | Viewed by 1104
Abstract
Dynamic vibration absorbers (DVAs) are extensively used in the prevention of building and bridge vibrations, as well as in vehicle suspension and other fields, due to their excellent damping performance. The reliable optimization of DVA parameters is key to improve their performance. In [...] Read more.
Dynamic vibration absorbers (DVAs) are extensively used in the prevention of building and bridge vibrations, as well as in vehicle suspension and other fields, due to their excellent damping performance. The reliable optimization of DVA parameters is key to improve their performance. In this paper, an H∞ optimization problem of a novel three-element-type DVA model including an inerter device and a grounded negative stiffness spring is studied by combining a traditional theory and an intelligent algorithm. Firstly, to ensure the system’s stability, the specific analytical expressions of the optimal tuning frequency ratio, stiffness ratio, and approximate damping ratio with regard to the mass ratio and inerter–mass ratio are determined through fixed-point theory, which provides an iterative range for algorithm optimization. Secondly, the particle swarm optimization (PSO) algorithm is used to further optimize the four parameters of DVA simultaneously. The effects of the traditional fixed-point theory and the intelligent PSO algorithm are comprehensively compared and analyzed. The results verify that the effect of the coupling of the traditional theory and the intelligent algorithm is better than that of fixed-point theory alone and can make the two resonance peaks on the amplitude–frequency response curves almost equal, which is difficult to achieve using fixed-point theory alone. Finally, we compare the proposed model with other DVA models under harmonic and random excitation. By comparing the amplitude–frequency curves, stroke lengths, mean square responses, time history diagrams, variances and decrease ratios, it is clear that the established DVA has a good vibration absorption effect. The research results provide theoretical and algorithm support for designing more effective DVA models of the same type in engineering applications. Full article
(This article belongs to the Special Issue New Trends in Theoretical and Mathematical Physics)
►▼ Show Figures

Figure 1

20 pages, 754 KiB  
Article
Hierarchical Wilson–Cowan Models and Connection Matrices
by W. A. Zúñiga-Galindo and B. A. Zambrano-Luna
Entropy 2023, 25(6), 949; https://doi.org/10.3390/e25060949 - 16 Jun 2023
Cited by 1 | Viewed by 998
Abstract
This work aims to study the interplay between the Wilson–Cowan model and connection matrices. These matrices describe cortical neural wiring, while Wilson–Cowan equations provide a dynamical description of neural interaction. We formulate Wilson–Cowan equations on locally compact Abelian groups. We show that the [...] Read more.
This work aims to study the interplay between the Wilson–Cowan model and connection matrices. These matrices describe cortical neural wiring, while Wilson–Cowan equations provide a dynamical description of neural interaction. We formulate Wilson–Cowan equations on locally compact Abelian groups. We show that the Cauchy problem is well posed. We then select a type of group that allows us to incorporate the experimental information provided by the connection matrices. We argue that the classical Wilson–Cowan model is incompatible with the small-world property. A necessary condition to have this property is that the Wilson–Cowan equations be formulated on a compact group. We propose a p-adic version of the Wilson–Cowan model, a hierarchical version in which the neurons are organized into an infinite rooted tree. We present several numerical simulations showing that the p-adic version matches the predictions of the classical version in relevant experiments. The p-adic version allows the incorporation of the connection matrices into the Wilson–Cowan model. We present several numerical simulations using a neural network model that incorporates a p-adic approximation of the connection matrix of the cat cortex. Full article
(This article belongs to the Special Issue New Trends in Theoretical and Mathematical Physics)
►▼ Show Figures

Figure 1

22 pages, 369 KiB  
Article
Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators
by Farrukh Mukhamedov, Izzat Qaralleh, Taimun Qaisar and Mahmoud Alhaj Hasan
Entropy 2023, 25(6), 934; https://doi.org/10.3390/e25060934 - 13 Jun 2023
Cited by 1 | Viewed by 880
Abstract
The present paper deals with a class of ξ(a)-quadratic stochastic operators, referred to as QSOs, on a two-dimensional simplex. It investigates the algebraic properties of the genetic algebras associated with ξ(a)-QSOs. Namely, the associativity, characters [...] Read more.
The present paper deals with a class of ξ(a)-quadratic stochastic operators, referred to as QSOs, on a two-dimensional simplex. It investigates the algebraic properties of the genetic algebras associated with ξ(a)-QSOs. Namely, the associativity, characters and derivations of genetic algebras are studied. Moreover, the dynamics of these operators are also explored. Specifically, we focus on a particular partition that results in nine classes, which are further reduced to three nonconjugate classes. Each class gives rise to a genetic algebra denoted as Ai, and it is shown that these algebras are isomorphic. The investigation then delves into analyzing various algebraic properties within these genetic algebras, such as associativity, characters, and derivations. The conditions for associativity and character behavior are provided. Furthermore, a comprehensive analysis of the dynamic behavior of these operators is conducted. Full article
(This article belongs to the Special Issue New Trends in Theoretical and Mathematical Physics)
►▼ Show Figures

Figure 1

8 pages, 267 KiB  
Article
On Geometry of p-Adic Coherent States and Mutually Unbiased Bases
by Evgeny Zelenov
Entropy 2023, 25(6), 902; https://doi.org/10.3390/e25060902 - 06 Jun 2023
Cited by 1 | Viewed by 875
Abstract
This paper considers coherent states for the representation of Weyl commutation relations over a field of p-adic numbers. A geometric object, a lattice in vector space over a field of p-adic numbers, corresponds to the family of coherent states. It is [...] Read more.
This paper considers coherent states for the representation of Weyl commutation relations over a field of p-adic numbers. A geometric object, a lattice in vector space over a field of p-adic numbers, corresponds to the family of coherent states. It is proven that the bases of coherent states corresponding to different lattices are mutually unbiased, and that the operators defining the quantization of symplectic dynamics are Hadamard operators. Full article
(This article belongs to the Special Issue New Trends in Theoretical and Mathematical Physics)
49 pages, 4386 KiB  
Article
Free Choice in Quantum Theory: A p-adic View
by Vladimir Anashin
Entropy 2023, 25(5), 830; https://doi.org/10.3390/e25050830 - 22 May 2023
Cited by 2 | Viewed by 1193
Abstract
In this paper, it is rigorously proven that since observational data (i.e., numerical values of physical quantities) are rational numbers only due to inevitably nonzero measurements errors, the conclusion about whether Nature at the smallest scales is discrete or continuous, random and chaotic, [...] Read more.
In this paper, it is rigorously proven that since observational data (i.e., numerical values of physical quantities) are rational numbers only due to inevitably nonzero measurements errors, the conclusion about whether Nature at the smallest scales is discrete or continuous, random and chaotic, or strictly deterministic, solely depends on experimentalist’s free choice of the metrics (real or p-adic) he chooses to process the observational data. The main mathematical tools are p-adic 1-Lipschitz maps (which therefore are continuous with respect to the p-adic metric). The maps are exactly the ones defined by sequential Mealy machines (rather than by cellular automata) and therefore are causal functions over discrete time. A wide class of the maps can naturally be expanded to continuous real functions, so the maps may serve as mathematical models of open physical systems both over discrete and over continuous time. For these models, wave functions are constructed, entropic uncertainty relation is proven, and no hidden parameters are assumed. The paper is motivated by the ideas of I. Volovich on p-adic mathematical physics, by G. ‘t Hooft’s cellular automaton interpretation of quantum mechanics, and to some extent, by recent papers on superdeterminism by J. Hance, S. Hossenfelder, and T. Palmer. Full article
(This article belongs to the Special Issue New Trends in Theoretical and Mathematical Physics)
►▼ Show Figures

Figure 1

9 pages, 268 KiB  
Article
Learning by Population Genetics and Matrix Riccati Equation
by Sergei Kozyrev
Entropy 2023, 25(2), 348; https://doi.org/10.3390/e25020348 - 14 Feb 2023
Cited by 2 | Viewed by 1009
Abstract
A model of learning as a generalization of the Eigen’s quasispecies model in population genetics is introduced. Eigen’s model is considered as a matrix Riccati equation. The error catastrophe in the Eigen’s model (when the purifying selection becomes ineffective) is discussed as the [...] Read more.
A model of learning as a generalization of the Eigen’s quasispecies model in population genetics is introduced. Eigen’s model is considered as a matrix Riccati equation. The error catastrophe in the Eigen’s model (when the purifying selection becomes ineffective) is discussed as the divergence of the Perron–Frobenius eigenvalue of the Riccati model in the limit of large matrices. A known estimate for the Perron–Frobenius eigenvalue provides an explanation for observed patterns of genomic evolution. We propose to consider the error catastrophe in Eigen’s model as an analog of overfitting in learning theory; this gives a criterion for the presence of overfitting in learning. Full article
(This article belongs to the Special Issue New Trends in Theoretical and Mathematical Physics)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-6
Back to TopTop