BIBLIOS

Document type
Journal articles

Document subtype
Full paper

Title
Many-body aspects of approach to equilibrium

Participants in the publication
Eric A. Carlen (Author)
RUTGERS UNIVERSITY
Dep. Matemática
CMAF
Maria C. Carvalho (Author)
Dep. Matemática
CMAF
Michael P. Loss (Author)

Summary
Kinetic theory and approach to equilibrium is usually studied in the realm of the Boltzmann equation. With a few notable exceptions not much is known about the solutions of this equation and about its derivation from fundamental principles. In 1956 Mark Kac introduced a probabilistic model of N interacting particles. The velocity distribution is governed by a Markov semi group and the evolution of its single particle marginals is governed (in the infinite particle limit) by a caricature of the spatially homogeneous Boltzmann equation. In joint work with Eric Carlen and Maria Carvalho we compute the gap of the generator of this Markov semigroup and show that the best possible rate of approach to equilibrium in the Kac model is precisely the one predicted by the linearized Boltzmann equation. Similar, but less precise results hold for maxwellian molecules.


Where published
Journées équations aux dérivées partielles

Publication Identifiers
ISSN - 0752-0360