The conference is in English.
Abstract
One of the guiding ideas of statistical physics is that the internal dynamics of systems composed of a large number of degrees of freedom is sufficiently chaotic to allow an equilibrium described by the statistical sets introduced by Boltzmann and Gibbs to be reached. In 1954, Fermi, Pasta and Ulam published the results of numerical simulations carried out with one of the very first computers. They showed that for initial conditions in which energy is initially concentrated in a few modes, even after a long time, this energy is not equipartitioned between all modes. This called into question the postulate underlying Boltzmann's and Gibbs' statistical ensembles, according to which a system reaches equilibrium through its own dynamics.
Giancarlo Benettin's seminar provided an update on this Fermi-Pasta-Ulam problem, which has been the subject of a large number of articles over the last half-century and is at the heart of current research into the anomalous Fourier law. The proximity of nonlinear oscillator models coupled with integrable models such as Toda's chain, the limited precision and relatively short duration of simulations have all been obstacles to clarifying this problem. One of the most striking results is the presence of two time scales ƒ: a short time scale where the energy of the initial condition is distributed over only a few modes (which had been observed in the Fermi, Pasta and Ulam paper) and a much longer time scale (inaccessible with 1950s computers) where equipartition is achieved.
