We consider a system weakly interacting with a bath as a thermodynamic
setting to establish a quantum foundation of statistical physics. It is shown
that even if the composite system is initially in an arbitrary nonequilibrium
pure quantum state, the unitary dynamics of a generic weak interaction almost
always drives the subsystem into the canonical ensemble, in the usual sense of
typicality. A crucial step is taken by assuming that the matrix elements of the
interaction Hamiltonian have random phases, while their amplitudes are left
unrestricted
