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Entropy production and convergence to equilibrium for the Boltzmann equation. (English) Zbl 1221.82082

Zambrini, Jean-Claude (ed.), XIVth international congress on mathematical physics (ICMP 2003), Lisbon, Portugal, 28 July – 2 August 2003. Selected papers based on the presentation at the conference. Hackensack, NJ: World Scientific (ISBN 981-256-201-X/hbk). 130-144 (2005).
Summary: In this short paper, I address recent developments in the study of convergence to equilibrium for the Boltzmann equation, linked with the study of Boltzmann’s \(H\) Theorem and entropy production. The presentation closely follows my lecture at the ICMP 2003 Conference in Lisbon. For pedagogy, I use an informal style, at the cost of losing rigor and precision; but details and rigorous discussion can be found in the research papers quoted within the text [see mainly the author, Commun. Math. Phys. 234, No. 3, 455–490 (2003; Zbl 1041.82018), and L. Desvillettes and the author, Invent. Math. 159, No. 2, 245–316 (2005; Zbl 1162.82316)].
For the entire collection see [Zbl 1089.81005].

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
82D05 Statistical mechanics of gases

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