A unified approach to kinetic description of processes in active systems
著者
書誌事項
A unified approach to kinetic description of processes in active systems
（Fundamental theories of physics, v. 67 . Statistical theory of open systems ; v. 1）
Kluwer Academic Publishers, c1995
- : PB
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注記
Bibliographical references: p. 557-569
内容説明・目次
- 巻冊次
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ISBN 9780792331995
内容説明
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 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. This text should be useful to postgraduate students and researchers in chemistry, physics, mathematics, economics, sociology, and engineering.
目次
Dynamic and Statistical Description of Processes in Macroscopic Systems. Statistical Theory of Equilibrium State. Distributions of Functions of Dynamic Variables. Fluctuations of Internal Parameters. Methods of Distribution Functions and Microscopic Phase Density. Boltzmann Kinetic Equation. From BBGKY Equations to Kinetic Equations for Boltzmann Gas. Kinetic Theory of Nonideal Gas. Kinetic Theory of Fluctuations. Langevin Method in Kinetic Theory of Fluctuations. From Kinetic Boltzmann Equation to Equations of Gas Dynamics. Thermodynamics of Nonequilibrium Irreversible Processes. Unified Description of Kinetic and Hydrodynamic Processes. Transition from Generalized Kinetic Equation to Equations of Gas Dynamics. Nonlinear Brownian Motion. Examples of Nonlinear Brownian Motion. Nonlinear Brownian Motion. Unified Description of Kinetic, Hydrodynamic and Diffusion Processes. Kinetic Theory of Active Media. Kinetic Theory of Fluctuations in Active Media. Anomalous Brownian Motion. Equilibrium and Nonequilibrium Natural Flicker Noise and Residual Time Correlations. Criteria of Self-Organization. Turbulent Motion. Kinetic Description of Turbulence. Bridge from Classical Statistical Theory of Open Systems to Quantum Theory.
- 巻冊次
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: PB ISBN 9780792332428
内容説明
Let us begin by quoting from the Preface to the author's Statistical Physics (Moscow, Nauka 1982; also published in English by Harwood in 1986): '''My God! Yet another book on statistical physics! There's no room on my bookshelves left!' Such emotionsare quite understandable. Beforejumping to conclusions, however, it would be worthwhile to read the Introduction and look through the table of contents. Then the reader will find that this book is totally different from the existing courses, fundamental and concise. ... We do not use the conventional division into statistical theories ofequilibrium and nonequilibrium states. Rather than that, the theory ofnonequilibrium state is the basis and the backbone oftheentirecourse. ... This approach allows us to develop a unified method for statistical description ofa very broadclassofsystems. ... The author certainly does not wish to exaggerate the advantages of the book, considering it asjustthe first attemptto create a textbookofa new kind." The next step in this direction was the author's Turbulent Motion and the Structure of Chaos (Moscow, Nauka 1990; Kluwer Academic Publishers 1991). This book is subtitled A New Approach to the Statistical Theory of Open Systems. Naturally, the "new approach" is not meant to defy the consistent and efficient methods of the conventional statistical theory; itshould be regarded as auseful reinforcementofsuch methods.
目次
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.
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