  This work addresses the problem of relaxation of open systems to
quasi-equilibrium states. Time-dependent density matrix of two arbitrary
coupled quantum oscillators of arbitrary properties interacting with separate
reservoirs is derived based on path integration. Temporal dynamics of spatial
variances and covariances of the oscillators from any given time up to
quasi-equilibrium steady states is studied. It is demonstrated for general case
that asymptotic spatial variances of two arbitrary oscillators and their
covariances achieve stationary values in the long-time limit. A comparison of
steady state characteristics of coupled oscillators with those predicted by the
fluctuation dissipation theorem (FDT) is performed. It is shown that the larger
the difference in masses and eigenfrequencies of coupled oscillators, the
smaller are the deviations of stationary variances from those given by the FDT
at fixed coupling strength and fixed difference in temperatures between thermal
baths. In framework of the model of the bilinear interaction and Ohmic
dissipation and at any oscillators parameters the variances and covariances
have divergent character at strong couplings.
