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Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1916)
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Table of contents (2 chapters)
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Front Matter
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Back Matter
About this book
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 molecular level.
During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.
Keywords
- Boltzmann equation
- H Theorem
- Stochastic Markov processes
- entropy
- interacting particle system
- kinetic limit
- partial differential equations
Reviews
Authors, Editors and Affiliations
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Laboratoire Jacques-Louis Lions (UMR CNRS 7598), Université Pierre et Marie Curie, Paris, France
François Golse
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Centre de recherche en mathématiques de la décision (UMR CNRS 7534), Université Paris - Dauphine, Paris Cedex 16, France
Stefano Olla
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Department of Mathematics Evans Hall, University of California, Berkeley, USA
Fraydoun Rezakhanlou
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Unité de mathématiques pures et appliquées (UMR CNRS 5669), Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France
Cédric Villani
Bibliographic Information
Book Title: Entropy Methods for the Boltzmann Equation
Book Subtitle: Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001
Authors: Fraydoun Rezakhanlou, Cédric Villani
Editors: François Golse, Stefano Olla
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-73705-6
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Softcover ISBN: 978-3-540-73704-9Published: 14 November 2007
eBook ISBN: 978-3-540-73705-6Published: 22 December 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 113
Topics: Probability Theory, Differential Equations, Theoretical, Mathematical and Computational Physics