Large Deviations in Physics: The Legacy of the Law of Large Numbers (Lecture Notes in Physics Book 885)

This book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence. Front Matter....Pages i-xiv From the Law of Large Numbers to Large Deviation Theory in Statistical Physics: An Introduction....Pages 1-27 Ergodicity: How Can It Be Broken?....Pages 29-70 Large Deviations in Stationary States, Especially Nonequilibrium....Pages 71-92 Fluctuation-Dissipation and Fluctuation Relations: From Equilibrium to Nonequilibrium and Back....Pages 93-133 Large Deviations in Disordered Spin Systems....Pages 135-160 Large Deviations in Monte Carlo Methods....Pages 161-191 Large Deviations Techniques for Long-Range Interactions....Pages 193-220 Large Deviations of Brownian Motors....Pages 221-241 Stochastic Fluctuations in Deterministic Systems....Pages 243-261 Anomalous Diffusion: Deterministic and Stochastic Perspectives....Pages 263-293 Large Deviations in Turbulence....Pages 295-310 Back Matter....Pages 311-314