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.

中文翻译：

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弱遍历系统的非平衡统计力学

讨论了哈密顿系统的吉布斯合奏的特性，该特性描述了紧凑配置流形上沿测地线的运动。我们引入了弱遍历系统，其配置空间上的功能时间平均几乎在任何地方都是恒定的。通常的遍历系统当然是弱遍历的，但事实并非如此。考虑了随着时间无限增加而使吉布斯集合体的密度和温度相等的一系列问题。另外，建立了具有间隔壁的长方体中的台球的弱遍历性。