Entropy Methods for the Boltzmann Equation Lectures from a Special S
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or
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Fraydoun Rezakhanlou · Cédric Villani
Entropy Methods for the Boltzmann Equation Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001
Editors: François Golse Stefano Olla
ABC
Authors and Editors Fraydoun Rezakhanlou
Cédric Villani
Department of Mathematics Evans Hall University of California Berkeley, CA 94720-3840, USA e-mail: [email protected]
Unité de mathématiques pures et appliquées (UMR CNRS 5669) Ecole Normale Supérieure de Lyon 46, allée d’Italie 69364 Lyon Cedex 07, France e-mail: [email protected]
François Golse
Stefano Olla
Laboratoire Jacques-Louis Lions (UMR CNRS 7598) Université Pierre et Marie Curie 175 rue du Chevaleret 75013 Paris, France e-mail: [email protected]
Centre de recherche en mathématiques de la décision (UMR CNRS 7534) Université Paris - Dauphine Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16, France e-mail: [email protected]
Library of Congress Control Number: 2007932803 Mathematics Subject Classification (2000): 76P05, 82B40, 94A15, 60K35, 82C22 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN 978-3-540-73704-9 Springer Berlin Heidelberg New York DOI 10.1007/978-3-540-73705-6 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2008 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting by the authors and SPi using a Springer LATEX macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
SPIN: 12092147
41/SPi
543210
Foreword
One of the major contributions of Ludwig Boltzmann to science has been the connection between time irreversibility and the increase of entropy as a welldefined quantity associated to the macroscopic state of a system. His ideas are at the basis of most studies in non-equilibrium statistical mechanics, and many non-equilibrium processes are still now physically understood in terms of their entropy production. More recently entropy and entropy production have become mathematical tools used in the context of kinetic and hydrodynamic limits, when deriving the macroscopic behavior of systems from the interaction dynamics of their (many) microscopic elementary
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