1 State-Dependent Noise and Interface Propagation.- 1.1 Introduction.- 1.2 The Blowtorch Theorem.- 1.3 Kink Motion.- 1.4 Temperature Inhomogeneity and Kink Motion.- 1.5 Conclusion.- 1.6 References.- 2 Stochastic Resonance and Its Precursors.- 2.1 Introduction.- 2.2 A Historical Overview.- 2.2.1 Ice-Ages Prelude.- 2.2.2 Stochastic Resonance in a Ring Laser.- 2.3 Linear-Response Theory.- 2.4 Precursors of Stochastic Resonance in Condensed Matter Physics.- 2.5 Stochastic Resonance in Periodically Driven Systems.- 2.6 Conclusions.- 2.7 Acknowledgments.- 2.8 References.- 3 Generation of Higher Harmonics in Noisy Nonlinear Systems.- 3.1 Introduction.- 3.2 Linear and Nonlinear Response of a Noisy Nonlinear System, General Theory.- 3.2.1 Linear Response Function.- 3.2.2 Nonlinear Response: Generation of Higher Harmonics.- 3.3 Noise-Induced Effects in the Generation of Higher Harmonics.- 3.3.1 Hopping-Induced Higher Harmonics Generation.- 3.3.2 Higher Harmonics Generation in Continuous Systems.- 3.4 Conclusions.- 3.5 Acknowledgments.- 3.6 References.- 4 Noise-Induced Linearization and Delinearization.- 4.1 Introduction.- 4.2 Physical Basis of Noise-Induced Linearization and Delinearization.- 4.3 Noise-Induced Linearization in an Overdamped Bistable System.- 4.4 Noise-Induced Delinearization in an Underdamped Monostable System.- 4.5 Conclusion.- 4.6 Acknowledgments.- 4.7 References.- 5 The Effect of Chaos on a Mean First-Passage Time.- 5.1 Introduction.- 5.2 Periodically Driven Rotor.- 5.3 The Hamiltonian.- 5.4 Mean First-Passage Time.- 5.5 Conclusions.- 5.6 Acknowledgments.- 5.7 References.- 6 Noise-Induced Sensitivity to Initial Conditions.- 6.1 Introduction.- 6.2 One-Degree-of-Freedom Systems.- 6.2.1 Dynamical Systems and the GMF.- 6.2.2 Additive Gaussian Noise.- 6.2.3 Other Forms of Noise.- 6.2.4 Average Flux Factor.- 6.2.5 Probability of Exit from a Safe Region.- 6.3 Mean Time Between Peaks-Brundsen-Holmes Oscillator.- 6.4 Higher-Degree-of-Freedom Systems.- 6.4.1 Slowly Varying Oscillators.- 6.4.2 A Spatially Extended System.- 6.5 Conclusions.- 6.6 Acknowledgment.- 6.7 References.- 7 Stabilization Through Fluctuations in Chaotic Systems.- 7.1 Introduction.- 7.2 Background.- 7.3 Chaos in Fast-Oscillating Frame of Reference.- 7.4 Closure of Reynolds-Type Equations Using the Stabilization Principle.- 7.5 Stable Representation of Chaotic Attractors.- 7.6 Acknowledgments.- 7.7 References.- 8 The Weak-Noise Characteristic Boundary Exit Problem: Old and New Results.- 8.1 Acknowledgments.- 8.2 References.- 9 Some Novel Features of Nonequilibrium Systems.- 9.1 References.- 10 Using Path-Integral Methods to Calculate Noise-Induced Escape Rates in Bistable Systems: The Case of Quasi-Monochromatic Noise.- 10.1 References.- 11 Noise-Facilitated Critical Behavior in Thermal Ignition of Energetic Media.- 11.1 Introduction and Review of Model Equations.- 11.2 Deterministic Model Equations for Thermal Ignition of Energetic Media.- 11.3 Stochastic Model Equations for Thermal Ignition of Energetic Media.- 11.4 Some Experimental Results and Discussion.- 11.5 Conclusions.- 11.6 References.- 12 The Hierarchies of Nonclassical Regimes for Diffusion-Limited Binary Reactions.- 12.1 Introduction.- 12.2 Initial Conditions and Difference Equation.- 12.2.1 Random and Correlated Initial Conditions.- 12.2.2 Solution of Difference Equations.- 12.2.3 Discretization.- 12.3 Method of Simulations.- 12.4 Kinetic Behavior for Random Initial Conditions.- 12.4.1 Kinetic Regimes.- 12.4.2 Crossovers.- 12.4.3 Comparison With Monte Carlo Simulations.- 12.5 Kinetic Behavior for Correlated Initial Conditions.- 12.5.1 Kinetic Regimes and Crossovers.- 12.5.2 Comparison With Monte Carlo Simulations.- 12.6 Summary.- 12.7 Appendix: Solution of Difference Equations.- 12.8 Appendix: Initial Averages.- 12.9 Acknowledgments.- 12.10 References.- 13 Scale Invariance in Epitaxial Growth.- 13.1 Introduction.- 13.2 The Lattice Model.- 13.3 Scaling in the Submonolayer Regime.- 13.4 Scali
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.
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