Turbulent motion and the structure of chaos : a new approach to the statistical theory of open systems

by Yu.L. Klimontovich ; [translated from the Russian by Alexander Dubroslavsky]


  • I.1. The Criteria of the Relative Degree of Order of the States of Open Systems.- I.2. Connection Between the Statistical and the Dynamic Descriptions of Motions in Macroscopic Open Systems. The Constructive Role of Dynamic Instability of Motion.- I.3. The Transition from Reversible to Irreversible Equations. The Gibbs Ensemble in the Statistical Theory of Nonequilibrium Processes.- I.4. The Role of Fluctuations at Different Levels of Description. Fluctuation Dissipation Relations.- I.5. Brownian Motion in Open Systems. Molecular and Turbulent Sources of Fluctuations.- I.6. Laminar and Turbulent Motion.- 1. Evolution of Entropy and Entropy Production in Open Systems.- 1.1. Chaos and Order. The Controlling Parameters. Physical Chaos. Evolution and Self-Organization in Open systems.- 1.2. Boltzmann-Shannon-Gibbs Entropy.- 1.3. Entropy Distribution Function.- 1.4. The Gibbs Ensemble. Smoothing over the Physically Infinitesimal Volume. Entropy Including Fluctuations. Space (Time) and Phase Averages. Local Ergodicity Condition.- 1.5. The Kinetic Boltzmann Equation for Statistical and Smoothed Distribuions. Physically Infinitesimal Scales. The Constructive Role of the Dynamic Instability of Motion of Atoms in a Gas.- 1.6. The Role of Nonequilibrium Fluctuations in a Boltzmann Gas. Molecular and Turbulent Sources of Fluctuations.- 1.7. The Kinetic Equations for the N-Particle Distribution Functions. The Leontovich Equation.- 1.8. Boltzmann's H-Theorem for Smoothed (Pulsating) and Deterministic Distributions.- 1.9. Entropy and Entropy Production for Smoothed and Deterministic Distributions.- 1.10. The Gibbs' Theorem.- 1.11. H-Theorem for Open Systems. Kulback Entropy.- 1.12. Evolution in the Space of Controlling Parameters. The S-Theorem.- 1.13. The S-Theorem. Local Formulation.- 1.14. The Comparison of the Relative Degree of Order of States on the Basis of the S-Theorem Using Experimental Data.- 1.15. Dynamic and Statistical Descriptions of Complex Motions. K-Entropy, Lyapunov Indices. Nonlinear Characteristics of the Trajectory Divergence.- 1.16. Criteria of Dynamic Instability of Motion in Statistical Theory.- 1.17. Entropy as Measure of Diversity in Biological Evolution.- 1.18. The Principle of Minimum Entropy Production in Self-Organization Processes.- 2. Transition From the Reversible Equations of Mechanics to the Irreversible Equations of the Statistical Theory.- 2.1. Two Types of Reversible Processes. Symmetry Properties of Distribution Functions.- 2.2. Liouville Equation and Vlasov Equation. The First Moments and the "Collisionless" Approximations.- 2.3. Reversible Equations in Quantum Statistical Theory.- 2.4. Two Types of Dissipative Kinetic Equations for N-Particle Distributions.- 2.5. Measure of Deficiency (Incompleteness) of the Statistical Description.- 2.6. The Hierarchy of Equations of Fluid Mechanics.- 3. Fluctuation Dissipation Relations.- 3.1. Examples of Fluctuation Dissipation Relations.- 3.2. FDR for N-Particle Distribution Functions.- 3.3. Thermodynamic Form of the FDR. The Callen-Welton Formula.- 3.4. FDR for a Boltzmann gas. The Fluctuative Representation of Boltzmann Collision Integral.- 3.5. FDR for Large-Scale (Kinetic) Fluctuations.- 3.6. Examples of FDR for Large-Scale Fluctuations.- 3.7. System of Quantum Atoms Oscillators.- 3.8. Fluctuation Dissipation Relations in Hydrodynamics.- 3.9. Two Ways of Defining Kinetic Coefficients.- 3.10. The Molecular Langevin Source in the Difffusion Equation.- 3.11. Connection between the Intensities of Langevin Sources and the Correlator of of Phase Density Fluctuations.- 3.12. Natural Flicker Noise ("1/f Noise"). FDR for Flicker Noise.- 3.13. Natural Flicker Noise and Superconductivity.- 4. Brownian Motion.- 4.1. Fokker-Planck and Langevin Equations.- 4.2. Three Definitions of the Langevin and Fokker-Planck Equations.- 4.3. The Fokker-Planck Equations in the Statistical Theory of Nonequilibrium Processes.- 4.4. Transition to the Fokker-Planck Equation from the Smoluchowski equation (the Chapman-Kolmogorov Equation) and from the Master Equation.- 4.5. Langevin.Sources in Kinetic Equations.- 4.6. Langevin Sources in Fokker-Planck and Einstein-Smoluchowski Equations.- 4.7. Turbulent Langevin Sources and Fluctuation Dissipation Relations in Hydrodynamics.- 4.8. Brownian Motion in Systems with a Variable Number of Particles..- 5. The Boltzmann-Gibbs-Shannon Entropy As Measure of the Relative Degree of Order in Open Systems.- 5.1. Van der Pol Generator.- 5.2. Generator with Inertial Nonlinearity.- 5.3. Invariant Measures. Examples of Gibbs Distributions for Open Systems.- 5.4. Generalized Van Der Pol Generators. Bifurcations of the Limiting Cycle Energy and the Period of Oscillations.- 5.5. Dynamic and Statistical Distributions.- 5.6. Comparison Between the Degrees of Order in the Bifurcation Points and in the State of Dynamic Chaos.- 5.7. Evolution of Entropy in Systems with Two Controlling Parameters.- 5.8. A Medium of Linked Generators. The Kinetic Approach in the Theory of Self-Organization.- 5.9. A System of Van der Pol Generators with Common Feedback. Associative Memory and Pattern Recognition.- 5.10. Kinetic Description of Chemically Reacting Systems.- 5.11. A Medium of Bistable Elements. The Kinetic Approach in the Theory of Phase Transitions.- 6. Turbulent Motion. The Structure of Chaos.- 6.1. Characteristic Features of Turbulent Motion. The Main Problems.- 6.2. Incompressible Fluid. Reynolds Equations. Reynolds Stresses.- 6.3. Well-Developed Turbulence. Turbulent Viscosity.- 6.4. Semiempirical Prandtl-Karman Theory of Turbulence.- 6.5. Onset of Turbulence in Steady Couette and Poiseuille Flows.- 6.6. Entropy Production in Laminar and Turbulent Flows.- 6.7. The Principle of Least Dissipation and the Principle of Minimum Entropy Production in Self-Organization Processes.- 6.8. Evolution of Entropy in the Transition from Laminar to Turbulent Flow.- 6.9. Kinetic Description of Hydrodynamic Motion.- Conclusion.- References.

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書名 Turbulent motion and the structure of chaos : a new approach to the statistical theory of open systems
著作者等 Klimontovich, I︠U︡. L.
Dubroslavsky A.
Klimontovich IU.L.
シリーズ名 Fundamental theories of physics
出版元 Kluwer Academic Publishers
刊行年月 c1991
ページ数 xi, 397 p.
大きさ 25 cm
ISBN 0792311140
NCID BA13192881
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言語 英語
原文言語 ロシア語
出版国 オランダ