# 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.

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