Self-Organization Autowaves and Structures Far from Equilibrium
According to its definition, Synergetics is concerned with systems that produce macroscopic spatial, temporal, or functional structures. Autowaves are·a specific, yet very important, case of spatio-temporal structures. The term "autowave" was coined in th
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Editor: Hermann Haken
Synergetics, an interdisciplinary field of research, is concerned with the cooperation of individual parts of a system that produces macroscopic spatial, temporal or functional structures. It deals with deterministic as well as stochastic processes. 1 Synergetics An Introduction 3rd Edition ByH. Haken 2 Synergetics A Workshop Editor: H. Haken 3 Synergetics Far from Equilibrium Editors: A. Pacault, C. Vidal 4 Structural Stability in Physics Editors: W. Giittinger, H. Eikemeier 5 Pattern Formation by Dynamic Systems and Pattern Recognition Editor: H. Haken 6 Dynamics of Synergetic Systems Editor: H. Haken 7 Problems of Biological Physics By L. A. Blumenfeld 8 Stochastic Nonlinear Systems in Physics, Chemistry, and Biology Editors: L. Arnold, R. Lefever 9 Numerical Methods in the Study of Critical Phenomena Editors: J. Della Dora, J. Demongeot, B. Lacolle 10 The Kinetic Theory of Electromagnetic Processes By Yu. L. Klimontovich 11 Chaos and Order in Nature Editor: H. Haken 12 Nonlinear Phenomena in Chemical Dynamics Editors: C. Vidal, A. Pacault 13 Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences By C. W. Gardiner 14 Concepts and Models of a Quantitative Sociology The Dynamics of Interacting Populations By W. Weidlich, G. Haag
15 Noise-Induced Transitions Theory and Applications in Physics, Chemistry, and Biology By W. Horsthemke, R. Lefever 16 Physics of Bioenergetic Processes By L. A. Blumenfeld 17 Evolution of Order and Chaos in Physics, Chemistry, and Biology Editor H. Haken 18 The Fokker-Planck Equation ByH. Risken 19 Chemical Oscillations, Waves, and Turbulence By Y. Kuramoto 20 Advanced Synergetics By H. Haken 21 Stochastic Phenomena and Chaotic Behaviour in Complex Systems Editor: P. Schuster 22 Synergetics - From Microscopic to Macroscopic Order Editor: E. Frehland 23 Synergetics of the Brain Editors: E. Ba~ar, H. Flohr, H. Haken, A. J. Mandell 24 Chaos and StatistiO)
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so that the neu transformed states A' P t " P' t will evolve under a Harkov process corresponding toW't for t(O and will thus exhibit monotonic increase of entropy in the "negative direction" of time. The dynamical fornu1ation of the second law of thermodynamics therefore consists of two statements: (1) first, it is the statement that the dynamical system admits two distinct A and A' so that the dynamical group Ut is transformed into t.1O distinct Harkov semigroups tit and W't corresponding to the tuo directions of time. Hisra and I have called this property intrinsic randomness. (2) In addition, there is a selection principle according to \lhich only one of these transformations gives rise to physically realizable states and physical evolution. This is a stronger property which we have called intrinsic irreversibility. The essential element \Ihich permits the construction of non10ca1 transformations A or A' is that of a suitable degree of instability (such as in K systems 7 ). Let us now indicate briefly how, in such types of systems, a monabe1ian algebra can be constructed and hml
