Univ. Paris-Saclay

Service de Physique de l'Etat Condensé

Will someone say exactly what Lanford's Theorem proves?
Giovanni Valente
Mardi 15/12/2009, 14:30
SPEC Bât 774, p.50, Orme des Merisiers

Boltzmann's equation is an outstanding result in the kinetic theory of gases, which Bolztmann derived from his celebrated H-theorem. Despite its long-standing legacy, the status of the latter had long remained an open issue. More than twenty years after its formulation, Culverwell inaugurated the famous debate in Nature with a provocative question: “Will anyone say exactly what the H-theorem proves?”. As a reaction to Loschmidt’s reversibility objection, Boltzmann formulated what later became known as statistical mechanics. Yet, the problem of giving a counterpart of Boltzmann’s results in such a new framework was left unsolved. As Uffink (2008) suggested, a theorem by Lanford (1975, 1976) would represent the only available candidate for a statistical version of H-theorem. However, this is proven for an extremely short time-length. Moreover, it relies on a set of probabilistic assumptions, whose status ought to be clarified. So, one may well ask: “Will anyone say exactly what Lanford’s theorem proves?”. In this talk we argue that Lanford’s result does provide a statistical H-theorem. It also shows that, under precise conditions, Boltzmann equation can be derived from Hamiltonian mechanics. Remarkably, no time-asymmetric ingredient would need to be added. Finally, we discuss a strategy to extend Lanford’s theorem to arbitrary time.

Contact : agrinbau


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