##
**Large scale dynamics of interacting particles.**
*(English)*
Zbl 0742.76002

Texts and Monographs in Physics. Berlin etc.: Springer-Verlag. xi, 342 p. with 19 fig. (1991).

The book considers a few important aspects of large scale description of interacting particle dynamics. This topic is treated from the viewpoint of two different approaches, so that the book itself is splitted into two parts. Part I deals with interacting particles governed by Newton’s equations of motion. The dynamics are deterministic but randomness enters through the initial conditions. The large scale dynamics are then given by the Boltzmann equation, and at low density deterministic chaos is not of a crucial importance. Part II treats stochastic lattice gases and related stochastic particle systems, as interacting Brownian particles and time-dependent Ginzburg-Landau models with a single conservation law. The main point is the derivation of the macroscopic equation and the fluctuation theory which itself splits into bulk fluctuations and the stochastic motion of a tracer particle.

The main chapters of the book are the following: Part 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.

Part II. Stochastic lattice gases. 1. Lattice gases with hard core exclusion; 2. Equilibrium fluctuations; 3. Nonequilibrium dynamics for reversible lattice gas; 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. Nonhydrodynamic limit dynamics.

The main chapters of the book are the following: Part 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.

Part II. Stochastic lattice gases. 1. Lattice gases with hard core exclusion; 2. Equilibrium fluctuations; 3. Nonequilibrium dynamics for reversible lattice gas; 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. Nonhydrodynamic limit dynamics.

Reviewer: Y.Kivshar (Düsseldorf)

### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76A02 | Foundations of fluid mechanics |

76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |

82-02 | Research exposition (monographs, survey articles) pertaining to statistical mechanics |

82C70 | Transport processes in time-dependent statistical mechanics |

82C22 | Interacting particle systems in time-dependent statistical mechanics |