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.

The core of the material on large scale dynamics of interacting particles grew out of courses I taught at the Katholieke Universiteit Leuven, Rutgers Universi- ty, and the Ludwig-Maximilians-Universitat Munchen and out of lectures I gave at the workshop "Hydrodynamical Behavior of Microscopic Systems" at the Universita dell'Aquila. I had the good luck of being helped through difficult ground by many friends. Amongst them I am deeply indebted to Joel L. Lebowitz. He got me started. Relatively little would have been achieved without his never-ending curiosity and insistence on clarity. Furthermore, I gratefully acknowledge the cooperation of Michael Aizenman, Henk van Beijeren, Carlo Boldrighini, Jean Bricmont, Paola Calderoni, Brian Davies, Anna DeMasi, Roland Dobrushin, Detlef Durr, Gregory Eyink, Mark Fannes, Pablo Ferrari, Alberto Frigerio, Joseph Fritz, Antonio Galves, Shelly Goldstein, Vittorio Gorini, Reinhard Illner, Claude Kipnis, Joachim Krug, Oscar Lanford, Reinhard Lang, Joel Lebowitz, Christian Maes, Stefano Olla, George Papanicolaou, Errico Presutti, Mario Pulvirenti, Fraydoun Rezakhanlou, Hermann Rost, Yasha Sinai, Yuri Suhov, Domo Szasz, Ragu Varadhan, Andre Verbeure, David Wick, and Horng-Tzer Yau. The list is somewhat lengthy, perhaps, but besides thanks I want to make clear that what I will describe is the outcome of a common scientific enterprise. I thank Henk van Beijeren and Detlef Durr for careful reading of and com- ments on a previous version. Paola Calderoni and Detlef Durr supplied me with the proof in Part I, Chapter 8. 4 which is most appreciated. Munchen, May 1991 Herbert Spohn Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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.