  In this paper we prove that Bose gas with weak pair interaction is non
ergodic system. In order to prove this fact we consider the divergences in some
nonequilibrium diagram technique. These divergences are analogous to the
divergences in the kinetic equations discovered by Cohen and Dorfman. We
develop the general theory of renormalization of such divergences and
illustrate it with some simple examples. The fact that the system is non
ergodic leads to the following consequence: to prove that the system tends to
the thermal equilibrium we should take into account its behavior on its
boundary. In this paper we illustrate this thesis with the Bogoliubov
derivation of the kinetic equations.
