Fluctuations and Order: The New Synthesis(Institute for Nonlinear Science)

The volume that you have before you is the result of a growing realization that fluctuations in nonequilibrium systems playa much more important role than was 1 first believed. It has become clear that in nonequilibrium systems noise plays an active, one might even say a creative, role in processes involving self-organization, pattern formation, and coherence, as well as in biological information processing, energy transduction, and functionality. Now is not the time for a comprehensive summary of these new ideas, and I am certainly not the person to attempt such a thing. Rather, this short introductory essay (and the book as a whole) is an attempt to describe where we are at present and how the viewpoint that has evolved in the last decade or so differs from those of past decades. Fluctuations arise either because of the coupling of a particular system to an ex- ternal unknown or "unknowable" system or because the particular description we are using is only a coarse-grained description which on some level is an approxima- tion. We describe the unpredictable and random deviations from our deterministic equations of motion as noise or fluctuations. A nonequilibrium system is one in which there is a net flow of energy. There are, as I see it, four basic levels of sophistication, or paradigms, con- cerning fluctuations in nature. At the lowest level of sophistication, there is an implicit assumption that noise is negligible: the deterministic paradigm.

Table of Contents:
1 State-Dependent Noise and Interface Propagation.- 2 Stochastic Resonance and Its Precursors.- 3 Generation of Higher Harmonics in Noisy Nonlinear Systems.- 4 Noise-Induced Linearization and Delinearization.- 5 The Effect of Chaos on a Mean First-Passage Time.- 6 Noise-Induced Sensitivity to Initial Conditions.- 7 Stabilization Through Fluctuations in Chaotic Systems.- 8 The Weak-Noise Characteristic Boundary Exit Problem: Old and New Results.- 9 Some Novel Features of Nonequilibrium Systems.- 10 Using Path-Integral Methods to Calculate Noise-Induced Escape Rates in Bistable Systems: The Case of Quasi-Monochromatic Noise.- 11 Noise-Facilitated Critical Behavior in Thermal Ignition of Energetic Media.- 12 The Hierarchies of Nonclassical Regimes for Diffusion-Limited Binary Reactions.- 13 Scale Invariance in Epitaxial Growth.- 14 Toward a Theory of Growing Surfaces: Mapping Two-Dimensional Laplacian Growth Onto Hamiltonian Dynamics and Statistics.- 15 Noise, Fractal Growth, and Exact Integrability in Nonequilibrium Pattern Formation.- 16 Order by Disorder and Topology in Frustrated Magnetic Systems.- 17 Noise-Induced Abnormal Growth.- 18 Clustering of Active Walkers: Phase Transition from Local Interactions.- 19 Brownian Combustion Engines.- 20 A Depolymerization Ratchet for Intracellular Transport.- 21 Order From Randomness: Spontaneous Firing From Stochastic Properties of Ion Channels.- 22 Simple Noise-Induced Transitions in Models of Neural Systems.- 23 Noise and Nonlinearity in Neuron Modeling.- 24 Physiological Singularities Modeled by Nondeterministic Equations of Motion and the Effect of Noise.- 25 Temporal Stochasticity Leads to Nondeterministic Chaos in a Model for Blood Cell Production.- 26 Quantum Noise in Gravitation and Cosmology.