  In the framework of the theory of open systems based on completely positive
quantum dynamical semigroups, we give a description of continuous variable
Gaussian R\'enyi-2 (GR2) quantum discord for a system consisting of two
non-interacting non-resonant bosonic modes embedded in a thermal environment.
In the case of both an entangled initial squeezed vacuum state and squeezed
thermal state, GR2 quantum discord has non-negative values for all temperatures
of the environment. We describe also the time evolution of GR2 classical
correlations and GR2 quantum mutual information of the quantum system. All
these quantities tend asymptotically to zero in the long time regime under the
effect of the thermal bath.
