FM 99-3 (version 0.2, 29 june 1999)

Author: Giovanni Gallavotti

Title: Ergodic and chaotic hypotheses: nonequilibrium ensembles in statistical
mechanics and turbulence

Abstract: The ergodic hypothesis outgrew from the ancient conception of motion
as periodic or quasi periodic. It did cause a revision of our views of motion,
particularly through Boltzmann and Poincar\'e: we discuss how Boltmann's
conception of motion is still very modern and how it can provide ideas and methods
to study the problem of nonequilibrium in mechanics and in fluids. This leads to the
chaotic hypothesis, a recent interpretation of a very ambitious principle conceived
by D. Ruelle: it is a possible extension of the ergodic hypothesis and it implies general
parameterless relations. Together with further ideas, it appears to be consistent with
some recent experiments as we discuss here.

Giovanni Gallavotti
Dipartimento di Fisica
Universit\'a di Roma ``La Sapienza''
P.le Moro 2, 00185 Roma, Italy
tel. +39-06-49914370