This book contains the invited papers of the interdisciplinary workshop on "Stochastic Nonlinear Systems in Physics, Chemistry and Biology" held at the Center for Interdisciplinary Research (ZIF), University of Bielefeld, West Germany, October 5-11, 1980. The workshop brought some 25 physicists, chemists, and biologists - who deal with stochastic phenomena - and about an equal number of mathematicians - who are experts in the theory of stochastic processes - together. The Scientific Commitee consisted of L. Arnold (Bremen), A. Dress (Bielefeld), W. Horsthemke (Brussels), T. Kurtz (Madison), R. Lefever (Brussels), G. Nicolis (Brussels), and V. Wihstutz (Bremen). The main topics of the workshop were the transition from deterministic to stoch­ astic behavior, external noise and noise induced transitions, internal fluctuations, phase transitions, and irreversible thermodynamics, and on the mathematical side, approximation of stochastic processes, qualitative theory of stochastic systems, and space-time processes. The workshop was sponsored by ZIF, Bielefeld, and by the Universities of Bremen and Brussels. We would like to thank the staff of ZIF and H. Crauel and M. Ehrhardt (Bremen) for the perfect organization and their assistance. In addition, our thanks go to Professor H. Haken for having these Proceedings included in the Se­ ries in Synergetics. Bremen and Brussels L. Arnold and R. Lefever December 1980 v Contents Part I. Introduction: From Deterministic to Stochastic Behavior On the Foundations of Kinetic Theory By B. Misr~ and I. Prigogine (With 1 Figure) ............................. .

Inhalt

I. Introduction: From Deterministic to Stochastic Behavior.- On the Foundations of Kinetic Theory.- Transition Phenomena in Nonlinear Systems.- II. Approximation of Stochastic Processes.- Approximation of Discontinuous Processes by Continuous Processes.- On the Asymptotic Behavior of Motions in Random Flows.- III. Description of Internal Fluctuations.- Some Aspects of Fluctuation Theory in Nonequilibrium Systems.- Aspects of Classical and Quantum Theory of Stochastic Bistable Systems.- Kinetics of Phase Separation.- Chemical Instabilities and Broken Symmetry: The Hard Mode Case.- IV. Long-Term Behavior of Stochastic Systems.- Asymptotic Behavior of Several Dimensional Diffusions.- Qualitative Theory of Stochastic Nonlinear Systems.- V. External Fluctuations and Noise Induced Transitions.- Noise Induced Transitions.- Noise Induced Transitions in Biological Systems.- Multiplicative Ornstein Uhlenbeck Noise in Nonequilibrium Phenomena.- VI. Stochastic Behavior in Model Systems.- Weak Turbulence in Deterministic Systems.- Stochastic Problems in Population Genetics: Applications of Itô's Stochastic Integrals.- Poisson Processes in Biology.- VII. Space-Time Processes and Stochastic Partial Differential Equations.- Linear Stochastic Evolution Equation Models for Chemical Reactions.- Stochastic Measure Processes.- VIII. Phase Transitions and Irreversible Thermodynamics.- Stochastic Methods in Non-Equilibrium Thermodynamics.- Fluctuation Dynamics Near Chemical Instabilities.- Transition Phenomena in Nonlinear Optics.- IX. Markov Processes and Time Reversibility.- Time-Reversibility in Dynamical Systems.- List of Participants.- Index of Contributors.