Ebook: Large Scale Dynamics of Interacting Particles

This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the derivation of large scale dynamics from microscopic models consisting of a very large number of interacting particles. In this monograph the author treats various macroscopic equations, in particular the Boltzmann equation for a low density fluid of hard spheres and the nonlinear diffusion equation for stochastic lattice gases. Also discussed are Gaussian fluctuations around the large scale deterministic motion, and the dynamics of tracer particles. The book addresses both researchers and students. Much of the material is presented here for the first time in book form.

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This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the derivation of large scale dynamics from microscopic models consisting of a very large number of interacting particles. In this monograph the author treats various macroscopic equations, in particular the Boltzmann equation for a low density fluid of hard spheres and the nonlinear diffusion equation for stochastic lattice gases. Also discussed are Gaussian fluctuations around the large scale deterministic motion, and the dynamics of tracer particles. The book addresses both researchers and students. Much of the material is presented here for the first time in book form.
Content:
Front Matter....Pages I-XI
Introduction....Pages 1-3
Front Matter....Pages 5-5
Dynamics....Pages 7-13
States of Equilibrium and Local Equilibrium....Pages 14-32
The Hydrodynamic Limit....Pages 33-47
Low Density Limit: The Boltzmann Equation....Pages 48-76
The Vlasov Equation....Pages 77-82
The Landau Equation....Pages 83-84
Time Correlations and Fluctuations....Pages 85-103
Dynamics of a Tracer Particle....Pages 104-150
The Role of Probability, Irreversibility....Pages 151-154
Front Matter....Pages 155-155
Lattice Gases With Hard Core Exclusion....Pages 157-174
Equilibrium Fluctuations....Pages 175-211
Nonequilibrium Dynamics for Reversible Lattice Gases....Pages 212-251
Nonequilibrium Dynamics of Driven Lattice Gases....Pages 252-261
Beyond the Hydrodynamic Time Scale....Pages 262-276
Tracer Dynamics....Pages 277-295
Stochastic Models with a Single Conservation Law Other than Lattice Gases....Pages 296-305
Non-Hydrodynamic Limit Dynamics....Pages 306-316
Back Matter....Pages 317-342

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This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the derivation of large scale dynamics from microscopic models consisting of a very large number of interacting particles. In this monograph the author treats various macroscopic equations, in particular the Boltzmann equation for a low density fluid of hard spheres and the nonlinear diffusion equation for stochastic lattice gases. Also discussed are Gaussian fluctuations around the large scale deterministic motion, and the dynamics of tracer particles. The book addresses both researchers and students. Much of the material is presented here for the first time in book form.
Content:
Front Matter....Pages I-XI
Introduction....Pages 1-3
Front Matter....Pages 5-5
Dynamics....Pages 7-13
States of Equilibrium and Local Equilibrium....Pages 14-32
The Hydrodynamic Limit....Pages 33-47
Low Density Limit: The Boltzmann Equation....Pages 48-76
The Vlasov Equation....Pages 77-82
The Landau Equation....Pages 83-84
Time Correlations and Fluctuations....Pages 85-103
Dynamics of a Tracer Particle....Pages 104-150
The Role of Probability, Irreversibility....Pages 151-154
Front Matter....Pages 155-155
Lattice Gases With Hard Core Exclusion....Pages 157-174
Equilibrium Fluctuations....Pages 175-211
Nonequilibrium Dynamics for Reversible Lattice Gases....Pages 212-251
Nonequilibrium Dynamics of Driven Lattice Gases....Pages 252-261
Beyond the Hydrodynamic Time Scale....Pages 262-276
Tracer Dynamics....Pages 277-295
Stochastic Models with a Single Conservation Law Other than Lattice Gases....Pages 296-305
Non-Hydrodynamic Limit Dynamics....Pages 306-316
Back Matter....Pages 317-342
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