Lanford’s Theorem and the Emergence of Irreversibility

2019-03-12 16:30
dipartimento di Matematica, aula consiglio VII piano

Martedì 12 marzo 2019, alle ore 16:30 precise

presso la Sala Consiglio (7 piano) del Dipartimento di Matematica,  Politecnico di Milano

in Via Bonardi 9



University of Minnesota

Abstract: It is a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A theorem by Lanford shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. This raises the question whether and how Lanford’s theorem succeeds in deriving this remarkable emergence of irreversibility. Many authors (Cercigniani, Illner & Pulvirenti, 1994; Lebowitz 1983, Spohn 1991) have expressed very different views on this question. In this talk, I will argue that the theorem actually does not imply irreversibility at all.



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