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This monograph gives a systematic presentation of ideas, methods and results of the modern statistical theory of open systems -- systems capable of exchanging matter, energy and information with the surrounding world. The resulting self-organization can lead to more sophisticated and advanced structures.
Central to this work are the statistical criteria of self-organization. The feasibility of a unified description of kinetic, hydrodynamic and diffusion processes in passive and active macroscopic systems without resorting to the methods of perturbation theory is demonstrated. On this basis, a general definition of thermal flux is given in terms of the entropy gradient. Moreover, a consistent method for calculating both kinetic and hydrodynamic fluctuations is proposed. This approach is then used to construct a theory of classical and anomalous Brownian motion in nonlinear media.
This theory makes it possible to treat in an original way the phenomenon of turbulence, and to propose a unified kinetic description of laminar and turbulent motion. The proposed methods are also applied to the statistical description of quantum macroscopic open systems. This provides answers as to whether or not the quantum mechanical description is complete, and whether or not there are hidden parameters in quantum mechanics. The book has no analogy in the existing literature. It is both a monograph and a textbook, and is based largely on the author's original research.
The book will be useful to postgraduate students and researchers in chemistry, physics, mathematics, economics, sociology, and engineering.
List of contents
Preface. 1. Introduction. 2. Dynamic and Statistical Description of Processes in Macroscopic Systems. 3. Statistical Theory of Equilibrium State. 4. Distributions of Functions of Dynamic Variables. Fluctuations of Internal Parameters. 5. Methods of Distribution Functions and Microscopic Phase Density. 6. Boltzmann Kinetic Equation. 7. From BBGKY Equations to Kinetic Equations for Boltzmann Gas. 8. Kinetic Theory of Nonideal Gas. 9. Kinetic Theory of Fluctuations. 10. Langevin Method in Kinetic Theory of Fluctuations. 11. From Kinetic Boltzmann Equation to Equations of Gas Dynamics. 12. Thermodynamics of Nonequilibrium Irreversible Processes. 13. Unified Description of Kinetic and Hydrodynamic Processes. 14. Transition from Generalized Kinetic Equation to Equations of Gas Dynamics. 15. Nonlinear Brownian Motion. 16. Examples of Nonlinear Brownian Motion. 17. Nonlinear Brownian Motion. Unified Description of Kinetic, Hydrodynamic and Diffusion Processes. 18. Kinetic Theory of Active Media. 19. Kinetic Theory of Fluctuations in Active Media. 20. Anomalous Brownian Motion. Equilibrium and Nonequilibrium Natural Flicker Noise and Residual Time Correlations. 21. Criteria of Self-Organization. 22. Turbulent Motion. Kinetic Description of Turbulence. 23. Bridge from Classical Statistical Theory of Open Systems to Quantum Theory. Conclusion. References.
