Self-Organization in Nonequilibrium Systems

Transcription

1 Self-Organization in Nonequilibrium Systems From Dissipative Structures to Order through Fluctuations G. Nicolis Universite Libre de Bruxelles Belgium I. Prigogine Universite Libre de Bruxelles Belgium and University of Texas at Austin Texas PHYSIKALISCHE BiBLIOTHEK FACHBEREICH 5 TECHNiSCHE HOCHSCHULE DARMSTADT 20 si A Wiley-Interscience Publication JOHN WILEY & SONS New York / London / Sydney / Toronto fur Theoretisdie FesfkSrperphysik Technische Hochschule Darmstadt

2 General Introduction PART I. THE THERMODYNAMIC BACKGROUND 1. Introduction General Comments, Open Systems, Conservation Equations Open Systems at Mechanical Equilibrium, The Mass-balance Equations, Thermodynamics of Irreversible Processes: The Linear Region Gibbs's Formula: Entropy Production, Phenomenological Relations: TheXinear Range of Irreversible Processes, Symmetry Properties of the Phenomenological Coefficients, Stationary Nonequilibrium States, Theorem of Minimum Entropy Production, Impossibility of Ordered Behavior in the Linear Range of Irreversible Processes, Diffusion, Nonlinear Thermodynamics Introduction, The General Evolution Criterion, Evolution Criterion and Kinetic Potential, Stability of Nonequilibrium States. Dissipative Structures, 55

3 vi PART II. MATHEMATICAL ASPECTS OF SELF- ORGANIZATION: DETERMINISTIC METHODS Contents 5. Systems Involving Chemical Reactions and Diffusion - Stability General Formulation, Lyapounov Stability, Orbital Stability, Structural Stability, Mathematical Tools Introduction, Theory of Bifurcations, Stability Theory, Theory of Catastrophes, Homogeneous Systems Involving Two Variables, Branchings, Bifurcations, and Limit Cycles, Simple Autocatalytic Models Two Intermediates, The Trimolecular Model (the " Brusselator "), Scaling, Steady States, and Boundary Conditions, Linear Stability Analysis, Bifurcation of Steady-state Dissipative Structures: General Scheme, Bifurcation: Fixed Boundary Conditions, Bifurcation: No-flux Boundary Conditions, Qualitative Properties of Dissipative Structures in Vicinity of First Bifurcation; Successive Instabilities and Secondary Bifurcations, Comparison with Computer Simulations, Localized Steady-state Dissipative Structures, Bifurcation of Time-periodic Dissipative Structures, Qualitative Properties of Time-periodic Dissipative Structures, Traveling Waves in Periodic Geometries, The Brusselator as a Closed System, Concluding Remarks, 158

4 8. Some Further Aspects of Dissipative Structures and Self-organization Phenomena Introduction, Conservative Oscillations, Simple Models Giving Rise to Limit Cycles, Multiple Steady States and All-or-none Transitions, Two-dimensional Problems, Systems Involving More than Two Chemical Variables, Coupled Oscillators, Heterogeneous Catalysis and Localized Transitions, Systems Involving Photochemical Steps, Some Further Methods of Analysis of Reaction-Diffusion Equations, Thermodynamic Aspects of Dissipative Structures, 212 PART III. STOCHASTIC METHODS 9. General Comments Introduction, Stochastic Formulation, Markovian Processes, Equilibrium Limit, Fluctuations in Nonequilibrium Systems: An Historical Survey, Birth-and-death Description of Fluctuations Master Equation for Birth-and-death Processes, Limitations of Birth-and-death Formalism, Some Methods of Analysis of Birth-and-death Master Equations, Moment Equations, Simple Examples, Systems Involving Two Stochastic Variables: The Lotka-Volterra Model, ConcludingTRemarlcs^ 272

5 viii Contents 11. Effect of Diffusion: Phase-space Description and Multivariate Master Equation Necessity for a Local Description of Fluctuations, Phase-space Description of Fluctuations, A Simple Model, Approximate Solution of Master Equation, Molecular Dynamics Studies of Fluctuations, Discussion, Reduction to a Multivariate Master Equation in Concentration Space, The Multivariate Master Equation in a Model System, Spatial Correlations in the Trimolecular Model, Critical Behavior, Concluding Remarks, A " Mean-field " Description of Fluctuations: Nonlinear Master Equation Introduction, Derivation of Nonlinear Master Equation, Further Properties and Moment Equations, Onset of a Limit Cycle, " Onset of a Spatial Dissipative Structure, Multiple Steady-state Transitions and Metastability, Asymptotic Solutions of Nonlinear Master Equation, Concluding Remarks, 334 PART IV. CONTROL MECHANISMS IN CHEMICAL AND BIOLOGICAL SYSTEMS 13. Self-organization in Chemical Reactions Introduction, Belousov-Zhabotinski Reaction: Experimental Facts, Mechanism, The "Oregonator", Oscillatory Behavior, Spatial Patterns, Briggs-Rauscher Reaction, 352

6 14. Regulatory Processes at the Subcellular Level Metabolic Oscillations, The Glycolytic Cycle, Allosteric Model for Glycolytic Oscillations, Limit-cycle Oscillations, Effect of External Distrubances on Limit-cycle Oscillation, Patterns of Spatiotemporal Organization in Allosteric Enzyme Model, Periodic Synthesis of camp, Reactions Involving Membrane-bound Enzymes, Physiological Significance of Metabolic Oscillations, 384 ix 15. Regulatory Processes at Cellular Level Introduction, Lac Operon, Mathematical Model for Induction of ^-Galactosidase, All-or-none Transitions, Catabolite Repression: Sustained Oscillations and Threshold Phenomena, Control of Cellular Division, Quantitative Model, Cellular Differentiation and Pattern Formation Introductory Remarks, Positional Information, Mechanisms Involved in Positional Information, Dissipative Structures and Onset of Polarity, A Quantitative Model, Positional Differentiation, Applications, 424 PART V. EVOLUTION AND POPULATION DYNAMICS 17. Thermodynamics of Evolution The Notion of Competition, Prebiotic Evolution: General Presentation, Prebiotic Polymer Formation, Biopolymer Competition and Hypercycles, 434

7 17.5. Evolution Viewed as a Problem of Stability, Evolutionary Feedback, Energy Dissipation in Simple Reaction Networks, A Biochemical Illustration, Thermodynamics of Ecosystems Introduction, Basic Equations, Example of Ordered Behavior: Organization in Insect Societies, Evolution of Ecosystems, Structural Instabilities and Increase of Complexity: Division of Labor, Stability and Complexity, 462 Perspectives and Concluding Remarks Introduction, Fluctuation Chemistry, Neural and Immune Networks, Immune Surveillance against Cancer, Social Systems and Epistemological Aspects, 472 References 475 Addendum: Mathematical Problems 487 Index 489