Large Scale Dynamics of Interacting Particles

Title page
Preface
Introduction
Scales
Outline
Part 1 Classical Particles
1. Dynamics
.1 Newtonian Dynamics
.2 Boundary Conditions
.3 Dynamics of Infinitely Many Partic1es
2. States of Equilibrium and Local Equilibrium
.1 Equilibrium Measures, Correlation Functions
.2 The Infinite Volume Limit
.3 Local Equilibrium States
.4 Local Stationarity
.5 The Static Continuum Limit
3. The Hydrodynamic Limit
.1 Propagation of Local Equilibrium
.2 Hydrodynamic Equations
.3 The Hard Rod Fluid
.4 Steady States
4. Low Density Limit: The Boltzmann Equation
.1 Low Density (Boltzmann-Grad) Limit
.2 BBGKY Hierarchy for Hard Spheres and Collision Histories
.3 Convergence of the Scaled Correlation Functions
.4 The Boltzmann Hierarchy
.5 Time Reversai
.6 Law of Large Numbers, Local Poisson
.7 The H-Function
.8 Extensions
5. The Vlasov Equation
6. The Landau Equation
7. Time Correlations and Fluctuations
.1 Fluctuation Fields
.2 The Green-Kubo Formula
.3 Transport for the Hard Rod Fluid
.4 The Fluctuating Boltzmann Equation
.5 The Fluctuating Vlasov Equation
8. Dynamics of a Tracer Particle
.1 Brownian Partic1e in a Fluid
.2 The Stationary Velocity Process
.3 Brownian Motion (Hydrodynamic) Limit
.4 Large Mass Limit
.5 Weak Coupling Limit
.6 Low Density Limit
.7 Mean Field Limit
.8 External Forces and the Einstein Relation
.9 Self-Diffusion
.10 Corrections to Markovian Limits
9. The Role of Probability, Irreversibility
Part II Stochastic Lattice Gases
1. Lattice Gases with Hard Core Exclusion
.1 Dynamics
.2 Stochastic Reversibility
.3 Invariant Measures, Ergodicity, Domains of Attraction
.4 Driven Lattice Gases
.5 Standard Models
2. Equilibrium Fluctuations
.1 Density Correlations and Bulk Diffusion
.2 The Green-Kubo Formula
.3 Currents
.4 The Gradient Condition
.5 Linear Response, Conductivity
.6 Steady State Transport
.7 State of Minimal Entropy Production
.8 Bounds on the Conductivity
.9 The Field of Density Fluctuations
.10 Scaling Limit for the Density Fluctuation Field (Proof)
.11 Critical Dynamics
3. Nonequilibrium Dynamics for Reversible Lattice Gases
.1 The Nonlinear Diffusion Equation
.2 Hydrodynamic Limit (Proof)
.3 Low Temperatures
.4 Weakly Driven Lattice Gases
.5 Nonequilibrium Fluctuations
.6 Local Equilibrium States and Minimal Entropy Production
.7 Large Deviations
4. Nonequilibrium Dynamics of Driven Lattice Gases
.1 Hyperbolic Equation of Conservation Type
.2 Asymmetric Exclusion Dynamics
.3 Fluctuation Theory
5. Beyond the Hydrodynamic Time Scale
.1 Navier-Stokes Correction for Driven Lattice Gases
.2 Local Structure of a Shock
.2.1 Macroscopic Equation with Fluctuations
.2.2 Shock in a Random Frame of Reference
.2.3 Shock in Higher Dimensions
6. Tracer Dynamics
.1 Two Component Systems
.2 Tracer Diffusion
.3 Convergence to Brownian Motion
.4 Nearest Neighbor lumps in One Dimension: The Case of Vanishing Self-Diffusion
7. Stochastic Models with a Single Conservation Law Other than Lattice Gases
.1 Lattice Gases Without Hard Core/Zero Range Dynamics
.2 Interacting Brownian Particles
.3 Ginzburg-Landau Dynamics
8. Non-Hydrodynamic Limit Dynamics
.1 Kinetic Limit
.2 Mean Field Limit
References
List of Mathematical Symbols
Subject Index