  The goal of this paper is to give a short review of recent results of the
authors concerning classical Hamiltonian many particle systems. We hope that
these results support the new possible formulation of Boltzmann's ergodicity
hypothesis which sounds as follows. For almost all potentials, the minimal
contact with external world, through only one particle of $N$, is sufficient
for ergodicity. But only if this contact has no memory. Also new results for
quantum case are presented.
