Atoms are considered basic building blocks of the material world. Computational modelling is a useful technique for studying and predicting natural events. Due to the complexity and wide scale range of particle systems, current computational modelling approaches, including Classical Mechanics, General Relativity, and Quantum Mechanics are separately designed to describe systems at different sizes and precisions. While these disparate models have practical value for discrete, domain-specific problems, lack of consistency between models results in challenges when multi-scale integration and computational scalability is required. In this paper, we proposed a novel theoretical framework, inspired by the communication theory of Shannon, to describe physical reality from a new perspective. We call this approach Communication Dynamics. As an initial demonstration of the relevancy of this model, we represent electron orbital structures of atoms. Our model aims to use a uniformly applicable mathematical formula to describe natural structures at different scales. We believe this information theoretical approach represents a new way to investigate particle-wave duality and opens a pathway to multi-scale model integration between physics and other fields of science. The appendix containing actual calculations is 141-page Wolfram Mathematica file, which can be obtained from SDPS web page.
Atoms are considered basic building blocks of the material world. Computational modelling is a useful technique for studying and predicting natural events. Due to the complexity and wide scale range of particle systems, current computational modelling approaches, including Classical Mechanics, General Relativity, and Quantum Mechanics are separately designed to describe systems at different sizes and precisions. While these disparate models have practical value for discrete, domain-specific problems, lack of consistency between models results in challenges when multi-scale integration and computational scalability is required. In this paper, we proposed a novel theoretical framework, inspired by the communication theory of Shannon, to describe physical reality from a new perspective. We call this approach Communication Dynamics. As an initial demonstration of the relevancy of this model, we represent electron orbital structures of atoms. Our model aims to use a uniformly applicable mathematical formula to describe natural structures at different scales. We believe this information theoretical approach represents a new way to investigate particle-wave duality and opens a pathway to multi-scale model integration between physics and other fields of science. The appendix containing actual calculations is 141-page Wolfram Mathematica file, which can be obtained from SDPS web page.
Connection is fundamental to understanding our world. Everything is expressed through connections: an object (matter) may be understood as a self-connection in the form of energy closed in on itself, while energy, information, and thoughts are forms of connection. We therefore proceed from connections to connection structures. In this approach, connections are more comprehensive than energy, and energy is more comprehensive than objects. Dynamic science is thus proposed as broader than traditional science because it is based on more general foundations. A central instrument of this approach is the format-number, which defines hierarchical structures of interpretations, energies, actions, and processes. Digitization of interpretation forms by format-numbers makes their use in digital technologies possible through appropriate programming. The format-number (2(1, 2, 1), (1, 2, 1)) characterizes the transition of quantum numbers through the tensor product to entanglement. The (1, 2)- and (2, 1)-interpretations are simplified models of a more complex reality. Beyond classical science, two approaches are distinguished: quantum mechanics, conditionally associated with the (1, 2)-interpretation, and dynamic mathematics, associated with the (2, 1)-interpretation. In contrast to the probabilistic approach of quantum mechanics, dynamic mathematics proposes a deterministic approach through an energy hierarchy. These approaches have a common “root” but operate from opposite positions and may lead to similar conclusions. The proposed framework extends the use of hierarchical structures beyond calculations to the manipulation of energies, objects, actions, and processes through higher levels. Interpretation formats are represented by format-numbers and quantum levels of connections. Traditional science, corresponding to the (1, 1)-interpretation, can be used for manipulating such numbers, thereby providing a bridge between dynamic and traditional science. The first task of the framework is to understand the hierarchy of energies in the Universe and the functioning principles of living energy, including living organisms and subtle energies. On this basis, artificial “pseudo-living energies” could be constructed. Dynamic science studies Energy-space with scalar product and norms of its elements described through format-numbers. Its mathematical basis emphasizes uncertainty and the dynamics of energy rather than objectivity alone. Mathematical uncertainties are used to form new structures for describing processes and objects that cannot be determined by conventional deterministic methods. Many energies are treated as indeterminate from the perspective of traditional science because they arise from uncertainties and may represent large concentrations of specific energy in chaotic states. Dynamic mathematics is designed to work with such uncertainties and proposes their manipulation using direct-accumulative, direct-parallel neural networks. Within this concept, a singular science realized through a neural network analogous to the human central nervous system would be more natural than ordinary computational approaches. Quantum computers are considered only an initial stage. The proposed SmnSprt network is intended to use format-numbers to construct or access levels of subtle energies, including transformations or “shifts” of ordinary energy into subtle energies. The practical development of such a network requires an instrumental mathematical basis and experimental verification. The aim of the work is therefore to introduce concepts and methods for developing new technologies based on this framework. Unlike classical mathematics, which focuses primarily on results, dynamic mathematics places the action itself at the center. It is intended not only to obtain results but also to directly control actions, especially within direct-parallel neural networks. The authors argue that any action has greater potential than its result and that this process-oriented view may be useful not only in mathematics and physics but also in other complex systems. The proposed apparatus is intended for studying living and subtle energies that are not directly expressed through ordinary objectivity and conventional forms of energy, although they may manifest themselves through lower levels. The significance of the work lies in offering a qualitatively different approach to complex processes through new mathematical, hierarchical, and dynamic structures, including processes studied in synergetics. The authors propose a presumptive mathematical structure and classification of subtle energies and introduce new classes of mathematical structures and singularities. The methodological distinction between classical and dynamic mathematics also concerns their application in technical devices. Classical mathematics operates indirectly through numbers, whereas dynamic mathematics is proposed to act directly through energies, including specific energies that determine numerical values at particular moments in technical systems. The uniqueness of a given energy is treated as a key feature for constructing and manipulating subtle energies. The authors do not claim that traditional science currently recognizes dynamic mathematics, since the two approaches occupy different perceptual positions. Traditional science and dynamic science are nevertheless regarded as intersecting domains. Dynamic models identified with traditional mathematics are termed dynamic mathematics, and the corresponding broader framework is termed dynamic science. Concepts such as self, oself, pself and other singularities are presented as instruments for creating order from chaos, while intention is treated as a mechanism for switching the assemblage point to a desired position.
Nihil est in intellectu quod non prius fuerit in sensu. The Physics of Information This book describes the limits for the communication of information with waves. How many ideas can we communicate by writing on a sheet of paper? How well can we hear a concert? How many details can we distinguish in an image? How much data can we get from our internet connection? These are all questions related to the transport of information by waves. Our sensing ability to capture the differences between distinct waveforms dictates the limits of the amount of information that is delivered by a propagating wave. The problem of quantifying this precisely requires a mathematical description and a physical understanding of both the propagation and the communication processes. We focus on the propagation of electromagnetic waves as described by Maxwell's theory of electromagnetism, and on communication as described by Shannon's theory of information. Although our treatment is mostly based on classical field theory, we also consider limiting regimes where the classical theory must give way to discrete quantum formulations. The old question of whether information is physics or mathematics resounds here. Information is certainly described mathematically, but we argue that it also has a definite physical structure. The central theme of this book is that Shannon's information-theoretic limits are natural. They are revealed by observing physical quantities at certain asymptotic scales where finite dimensionality emerges and observational uncertainties are averaged out. These limits are also rigorous, and obey the mathematical rules that govern the model of reality on which the physical theories are based. Shannon's Laws Originally introduced by Claude Elwood Shannon in 1948, and continuing up to its latest developments in multi-user communication networks, information theory describes in the language of mathematics the limits for the communication of information. These limits are operational, of real engineering significance, and independent of the semantic aspects associated with the communication process.
While theoretical ideas from quantum information science have long provided a foundation for understanding communication protocols and thermalization in many-body systems, the advent of near-term quantum devices offers the prospect of application and experimental study. In this thesis, we explore their interplay. The postulates of quantum mechanics generalize classical probability distributions and thus transmission of information, enabling fundamentally novel protocols for communication and cryptography. These algorithms motivate the deployment of quantum networks, a distributed model of computation where universality and fault-tolerance are often not required. We revisit the application of astronomical interferometry and provide a practical scheme based on distributed source coding, enabling powerful telescopes. Based on constructions from communication complexity, we design a voting scheme with efficient scaling of quantum communication and computation, and prove its security. The spread of quantum correlations, besides underlying the performance of many communication protocols, characterizes the process of objects away from equilibrium attaining a uniform state. Evolution is natural, requiring little control and easing study by quantum simulators. We analyze traversable wormholes, initially motivated by gauge-gravity duality, from this perspective. The effect of a gravitational scrambling mechanism is distinguished from generic mixing. Nonetheless, transfer of information is still found in common many-body systems, such as interacting spins. The two themes above are accompanied by proposals for physical realization in atomic and optical platforms. Communication protocols are carried out by photons transmitting quantum information and cavities mediating processing by atomic qubits. Thermalization is studied in strongly interacting systems of Rydberg atoms controlled by electromagnetic fields. These platforms represent the current generation of quantum computers, and so we probe its capabilities.
Scientists often refer to matter, energy, and information as the three basic categories, though they are related by various scientific laws. Compared to the concepts of matter and energy, the scientific definition of information is relatively new: it was only in the 1940s that Claude Shannon introduced the definition of information as a reduction of uncertainty, laying the foundation for modern information theory. In molecular electronic structure theory, we routinely encounter nonnegative quantities that sum to unity, forming valid probability distributions. These include properly normalized electron densities, eigenvalues of reduced density matrices, squared wave function coefficients in orthonormal bases, and related quantities. The incorporation of information-theoretic concepts into quantum chemistry has yielded profound insights into electronic system behavior. The two dominant frameworks in electronic structure theory are quantum many-body theory and density functional theory. This thesis systematically integrates these approaches with: classical information theory, yielding the information-theoretic approach, and quantum information theory, generating distinct tools like orbital entanglement measures and quantum fidelity metrics. In this thesis, we subsequently demonstrate applications of these information-theoretic methods in quantum chemistry for analyzing electronic structure and chemical phenomena.
Modern physical picture of the world is a quantum field and requires specific conceptual and mathematical apparatus. Practically, each concept is supplied by means of some mathematical structures from branches of mathematical and functional analysis, for the qualitative understanding which required independent decision by the student to practice specific physical problems. Design of information models of the physical processes allows us to comprehend the task as the object or phenomenon of the physical reality, to analyze it using various mathematical methods, to develop algorithm and the program of the interchange on the computer. The file contains data on the calculation of the wave functions of the first three stationary states of an electron in a potential well of a special type, which were presented in work Turinov A., Galdina A. Application Of Computer Modeling To Solving Quantum-Mechanical Problems // Physical and Mathematical Education : scientific journal. – 2017. – Issue 3(13). – Р. 170-177 (available at https://fmo-journal.fizmatsspu.sumy.ua/journals/2017-v3-13/2017_3-13-TurinovGaldina_Scientific_journal_F.pdf). Calculations were made in Wolfram Mathematica. The energies of these states were also calculated and the corresponding graphs were plotted.
This research introduces our innovative concept of using Orbius Path [1] and road path possibilities within quantum dynamics, in the broader context of quantum physics and quantum chip design. We emphasize that our innovative Orbius structural and topological properties of electron density distributions, together with trajectory-based descriptions of quantum behavior, offer a useful framework for understanding the physical requirements of next-generation quantum hardware. By integrating ideas from quantum chemistry, condensed matter physics, and quantum information science, our research introduces how static Orbius-Orbital-Bonding Topology and dynamic particle pathways may jointly influence coherence, entanglement, teleportation, and computational stability in quantum devices. The central premise of this research paper is that quantum chips require not only advanced fabrication techniques but also deeper theoretical insight into the behavior of matter at the nanoscale. In particular, our research study considers Orbius Orbital Bond Path in quantum chips can be used as a theoretical lens for examining electron transport, local bonding environments, and interconnectivity in quantum systems. At the same time, road path dynamics, understood through path-integral reasoning, offer a complementary way of describing the probabilistic motion of particles and the range of possible quantum trajectories. Together, these two perspectives suggest a dual framework Orbius Topological Pathway [1] for analyzing all possible quantum trajectory pathway between path-integral trajectory at atomic-scale structure and bonding topology device-level with quantum dynamics performance in quantum chips design. In addition, this research paper further proposes Orbius Orbital Path Engineering as a conceptual approach for designing quantum computing chips with enhanced stability, coherence preservation, and scalability. Our innovative Orbius Framework aims to provide a theoretical contribution to quantum device architecture by linking topological electron density analysis with the practical needs of qubit (1, 0 and 0, 1) systems. Our research study therefore offers a multidisciplinary perspective on how quantum bonding, pathway dynamics, and nanostructured materials may inform future developments in high-performance quantum processors.