Variation Principle in Informational Macrodynamics

ISBN-13: 9781402074653 / Angielski / Twarda / 2003 / 266 str.

Vladimir S. Lerner

Opis

Information Macrodynamics (IMD) belong to an interdisciplinary science that represents a new theoretical and computer-based methodology for a system informational descriptionand improvement, including various activities in such areas as thinking, intelligent processes, communications, management, and other nonphysical subjects with their mutual interactions, informational superimposition, and theinformation transferredbetweeninteractions. The IMD is based on the implementation of a single concept by a unique mathematical principle and formalism, rather than on an artificial combination of many arbitrary, auxiliary concepts and/or postulates and different mathematical subjects, such as the game, automata, catastrophe, logical operations theories, etc. This concept is explored mathematically using classical mathematics as calculus of variation and the probability theory, which are potent enough, without needing to developnew, specifiedmathematical systemicmethods. The formal IMD model automatically includes the related results from other fields, such as linear, nonlinear, collective and chaotic dynamics, stability theory, theory of information, physical analogies of classical and quantum mechanics, irreversible thermodynamics, andkinetics. The main IMD goal is to reveal the information regularities, mathematically expressed by the considered variation principle (VP), as a mathematical tool to extractthe regularities and define the model, whichdescribes theregularities. The IMD regularities and mechanisms are the results of the analytical solutions and are not retained by logical argumentation, rational introduction, and a reasonable discussion. The IMD's information computer modeling formalism includes a human being (as an observer, carrier and producer ofinformation), with a restoration of the model during the objectobservations.

Spis treści

Preface. I: The IMD Essence And Concepts. 1. Introduction. 1.1. Notion of Information. 1.2. Information Modeling. 2. The Information Modeling Concepts. 2.1. Initial Statements and Starting Points. 2.2. The Modeling Mechanism. 2.3. The Macromodel's Structure and Organization. 2.4. The Model's Controls, Joint Optimal Synthesis and Model's Identification. 2.5. The Model's Chaotic and Quantum Phenomena. 2.6. Region of Uncertainty and Systemic Invariants. 2.7. Compression of the Incoming Information. 2.8. The Evaluation of Information Contributions into the IN's Structure. 2.9. The Optimal Code's Language. 2.10. An Initial Triplet as a Carrier of the Total Macrostructure's Genetic Information. 2.11. Macrosystemic Complexity. 3. General Macrosystemic Functions. 3.1. Systemic Generalizations. 3.2. Mutation, Diversity, and Adaptation. 3.3. The Macroprocess' Evolution. 3.4. Robustness, Selection, Competition, Cooperation, and Self-Organization. 3.5. The Transformation of Imaginary into Real Information, Connection to Quantum Mechanics and Evolution. 3.6. Information Structure of the Control Mechanisms of the Cyclic Evolution. 3.7. Mechanism of Assembling the Node's Frequencies and Automatic Selection. 3.8. The Cyclic Model's Information Mechanisms. 3.9. Examples of the DSS' codes. 3.10. An Evaluation of Maximum Information Delivered from Environment. 3.11. About a Life-Time Duration of the IMD Model. 4. Main Macrosystemic Equations and Information Analogies. 4.1. Marcovian Processes and Equations of Math Physics. 4.1a. Examples of Extremal Principles. 4.2. An Analogy with the Feynman Path Functional in Quantum Mechanics. 4.3. Minimax Principle. 4.4. Macrolevel Dynamics. 4.5. Information Mass. 4.6. Information Forces. 4.7. The Information Virtual and Physical Connections. 4.8. The Invariant Transformation of the Model's Eigenvalues. 4.9. The Informational Analogies of Physical Invariants. 4.10. The Bound Energy of Information Cooperation. 5. The IMD's Relations to the Fundamental Sciences. 5.1. Classical Mechanics. 5.2. Special Theory of Relativity (TR). 5.3. Quantum and Statistical Mechanics. 5.4. Gravitation Theory. 5.5. String Theory. 5.6. Theory of Phase Transformations. 5.7. Theory of Stability. 5.8. Dynamic Systems Theory and Kolmogorov's Complexity. 5.9. Chaotic Dynamics. 5.10. Nonequilibrium Thermodynamics (NT). 5.10a. The NT and IMD Connections: Evolution Process of the Earth. 5.11. Statistical Physics and Equilibrium Thermodynamics. 5.13. General and Information Science. References. II: Mathematical Foundation Of Informational Macrodynamics. 1. Variation Problem for Dynamic Informational Modeling of Random Process. 1.1. Initial Mathematical Models and Statements. 1.2. The Probabilistic Evaluation of Micro-and Macrolevel's Processes. 1.3. Solution of the Variation Problem. References. 2. The Space Distributed Macromodel. 2.1. The Information Macrofunctional and the Euler-Ostrogradsky Equations. 2.2. The Invariant Conditions at