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 (Boltzmann-Grad)
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 Green-Kubo 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.- 8.5 Weak Coupling Limit.- 8.6 Low Density Limit.- 8.7 Mean
Field Limit.- 8.8 External Forces and the Einstein Relation.- 8.9
Self-Diffusion.- 8.10 Corrections to Markovian Limits.-
9. The Role of
Probability, Irreversibility.- II Stochastic Lattice Gases.-
1. Lattice Gases
with Hard Core Exclusion.- 1.1 Dynamics.- 1.2 Stochastic Reversibility.- 1.3
Invariant Measures, Ergodicity, Domains of Attraction.- 1.4 Driven Lattice
Gases.- 1.5 Standard Models.-
2. Equilibrium Fluctuations.- 2.1 Density
Correlations and Bulk Diffusion.- 2.2 The Green-Kubo Formula.- 2.3 Currents.-
2.4 The Gradient Condition.- 2.5 Linear Response, Conductivity.- 2.6 Steady
State Transport.- 2.7 State of Minimal Entropy Production.- 2.8 Bounds on the
Conductivity.- 2.9 The Field of Density Fluctuations.- 2.10 Scaling Limit for
the Density Fluctuation Field (Proof).- 2.11 Critical Dynamics.-
3.
Nonequilibrium Dynamics for Reversible Lattice Gases.- 3.1 The Nonlinear
Diffusion Equation.- 3.2 Hydrodynamic Limit (Proof).- 3.3 Low Temperatures.-
3.4 Weakly Driven Lattice Gases.- 3.5 Nonequilibrium Fluctuations.- 3.6 Local
Equilibrium States and Minimal Entropy Production.- 3.7 Large Deviations.-
4.
Nonequilibrium Dynamics of Driven Lattice Gases.- 4.1 Hyperbolic Equation of
Conservation Type.- 4.2 Asymmetric Exclusion Dynamics.- 4.3 Fluctuation
Theory.-
5. Beyond the Hydrodynamic Time Scale.- 5.1 Navier-Stokes Correction
for Driven Lattice Gases.- 5.2 Local Structure of a Shock.- 5.2.1 Macroscopic
Equation with Fluctuations.- 5.2.2 Shock in a Random Frame of Reference.-
5.2.3 Shock in Higher Dimensions.-
6. Tracer Dynamics.- 6.1 Two Component
Systems.- 6.2 Tracer Diffusion.- 6.3 Convergence to Brownian Motion.- 6.4
Nearest Neighbor Jumps in One Dimension: The Case of Vanishing
Self-Diffusion.-
7. Stochastic Models with a Single Conservation Law Other
than Lattice Gases.- 7.1 Lattice Gases Without Hard Core/Zero Range
Dynamics.- 7.2 Interacting Brownian Particles.- 7.3 Ginzburg-Landau
Dynamics.-
8. Non-Hydrodynamic Limit Dynamics.- 8.1 Kinetic Limit.- 8.2 Mean
Field Limit.- References.- List of Mathematical Symbols.
Biežāk uzdotie jautājumi par e-grāmatām