  The non-equilibrium state of two oscillators with a mutual interaction and
coupled to separate heat baths is discussed. Bosonic baths are considered, and
an exact spectral representation for the elements of the covariance matrix is
provided analytically. A wide class of spectral densities for the relevant bath
modes is allowed for. The validity of the fluctuation-dissipation theorem is
established for global equilibrium (both baths at the same temperature) in the
stationary state. Spectral measures of entanglement are suggested by comparing
to the equilibrium spectrum of zero-point fluctuations. No rotating-wave
approximation is applied, and anomalous heat transport from cold to hot bath,
as reported in earlier work, is demonstrated not to occur.
