We consider an arbitrary quantum system coupled non perturbatively to a large
arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges,
Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an
embedded quantum system was established for several classes of random
interactions. In other words, the time evolution of its quantum state does not
depend on the microscopic details of the interaction. Focusing at the long time
regime, we use this property to calculate analytically a new partition function
characterizing the stationary state and involving the overlaps between
eigenvectors of a bare and a dressed Hamiltonian. This partition function
provides a new thermodynamical ensemble which includes the microcanonical and
canonical ensembles as particular cases. We check our predictions with
numerical simulations.Comment: 1 figure, 5 pages. This article supersedes the part on the
equilibrium state in arXiv:1510.0435
