  We present a study that addresses both the stationary properties of the
energy current and quantum correlations in a three-mode chain subjected to
Ohmic and super-Ohmic dissipa- tions. An extensive numerical analysis shows
that the mean value and the fluctuations of the energy current remain
insensitive to the emergence of a rich variety of quantum correlations: such
as, two-mode discord and entanglement, bipartite three-mode and genuine
tripartite entanglement. The discussion of the numerical results is based on
the derived expressions for the stationary properties in terms of the two-time
correlation functions of the oscillator operators, which carry quantum
correlations. Interestingly, we show that quantum discord can be enhanced by
both considering initially squeezed thermal bath states and imposing
temperature gradients.
