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Nonequilibrium statistical mechanics of weakly ergodic systems. (English) Zbl 1471.82007
Summary: The properties of the Gibbs ensembles of Hamiltonian systems describing the motion along geodesics on a compact configuration manifold are discussed. We introduce weakly ergodic systems for which the time average of functions on the configuration space is constant almost everywhere. Usual ergodic systems are, of course, weakly ergodic, but the converse is not true. A range of questions concerning the equalization of the density and the temperature of a Gibbs ensemble as time increases indefinitely are considered. In addition, the weak ergodicity of a billiard in a rectangular parallelepiped with a partition wall is established.
82C03 Foundations of time-dependent statistical mechanics
82C23 Exactly solvable dynamic models in time-dependent statistical mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
Full Text: DOI
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