Large Scale Dynamics of Interacting Particles

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.- 2. States of Equilibrium and Local Equilibrium.- 3. The Hydrodynamic Limit.- 4. Low Density Limit: The Boltzmann Equation.- 5. The Vlasov Equation.- 6. The Landau Equation.- 7. Time Correlations and Fluctuations.- 8. Dynamics of a Tracer Particle.- 9. The Role of Probability, Irreversibility.- II Stochastic Lattice Gases.- 1. Lattice Gases with Hard Core Exclusion.- 2. Equilibrium Fluctuations.- 3. Nonequilibrium Dynamics for Reversible Lattice Gases.- 4. Nonequilibrium Dynamics of Driven Lattice Gases.- 5. Beyond the Hydrodynamic Time Scale.- 6. Tracer Dynamics.- 7. Stochastic Models with a Single Conservation Law Other than Lattice Gases.- 8. Non-Hydrodynamic Limit Dynamics.- References.- List of Mathematical Symbols.