Large Scale Dynamics of Interacting Particles [Paperback]

This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the explanation of large-scale dynamics (evolution differential equations) from models of a very large number of interacting particles. This book addresses both researchers and students. Much of the material presented has never been published in book-form before.This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the explanation of large-scale dynamics (evolution differential equations) from models of a very large number of interacting particles. This book addresses both researchers and students. Much of the material presented has never been published in book-form before.Scales.- Outline.- I Classical Particles.- 1. Dynamics.- 1.1 Newtonian Dynamics.- 1.2 Boundary Conditions.- 1.3 Dynamics of Infinitely Many Particles.- 2. States of Equilibrium and Local Equilibrium.- 2.1 Equilibrium Measures, Correlation Functions.- 2.2 The Infinite Volume Limit.- 2.3 Local Equilibrium States.- 2.4 Local Stationarity.- 2.5 The Static Continuum Limit.- 3. The Hydrodynamic Limit.- 3.1 Propagation of Local Equilibrium.- 3.2 Hydrodynamic Equations.- 3.3 The Hard Rod Fluid.- 3.4 Steady States.- 4. Low Density Limit: The Boltzmann Equation.- 4.1 Low Density (BoltzmannGrad) Limit.- 4.2 BBGKY Hierarchy for Hard Spheres and Collision Histories.- 4.3 Convergence of the Scaled Correlation Functions.- 4.4 The Boltzmann Hierarchy.- 4.5 Time Reversal.- 4.6 Law of Large Numbers, Local Poisson.- 4.7 The H-Function.- 4.8 Extensions.- 5. The Vlasov Equation.- 6. The Landau Equation.- 7. Time Correlations and Fluctuations.- 7.1 Fluctuation Fields.- 7.2 The GreenKubo Formula.- 7.3 Transport for the Hard Rod Fluid.- 7.4 The Fluctuating Boltzmann Equation.- 7.5 The Fluctuating Vlasov Equation.- 8. Dynamics of a Tracer Particle.- 8.1 Brownian Particle in a Fluid.- 8.2 The Stationary Velocity Process.- 8.3 Brownian Motion (Hydrodynamic) Limit.- 8.4 Large Mass Limit.- 8.lÃ#