Nonequilibrium Statistical Mechanics of Weakly Ergodic Systems

    2020, Volume 25, Number 6, pp.  674-688

    Author(s): Kozlov V. V.

    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.
    Keywords: Hamiltonian system, Liouville and Gibbs measures, Gibbs ensemble, weak ergodicity, mixing, billiard in a polytope
    Citation: Kozlov V. V., Nonequilibrium Statistical Mechanics of Weakly Ergodic Systems, Regular and Chaotic Dynamics, 2020, Volume 25, Number 6, pp. 674-688

    Access to the full text on the Springer website