In this paper we prove that Bose gas with weak pair interaction is nonergodic 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 nonergodic 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.
D. V. Prokhorenko. "On nonergodic property of Bose gas with weak pair interaction." J. Phys. Math. 1 1 - 31, December 2009. https://doi.org/10.4303/jpm/S090701