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Publication details

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 - Centro de Matemática e Aplicações Fundamentais 
Maria C. Carvalho (Author)
Dep. Matemática
CMAF - Centro de Matemática e Aplicações Fundamentais 
Michael P. Loss (Author)

Scope
International

Refereeing
Yes

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.

Date of Publication
2000

Where published
Journées équations aux dérivées partielles

Publication Identifiers
ISSN - 0752-0360

Number of pages
12


Export

APA
Eric A. Carlen, Maria C. Carvalho, Michael P. Loss, (2000). Many-body aspects of approach to equilibrium. Journées équations aux dérivées partielles, ISSN 0752-0360. eISSN .

IEEE
Eric A. Carlen, Maria C. Carvalho, Michael P. Loss, "Many-body aspects of approach to equilibrium" in Journées équations aux dérivées partielles, 2000.

BIBTEX
@article{45057, author = {Eric A. Carlen and Maria C. Carvalho and Michael P. Loss}, title = {Many-body aspects of approach to equilibrium}, journal = {Journées équations aux dérivées partielles}, year = 2000, }