  We investigate the link between the irreversibility generated by a stationary
dissipative process and the correlations established within a composite quantum
system. We provide two equivalent expressions for the entropy generated in the
non-equilibrium steady state of coupled quantum harmonic oscillators that allow
for a simple interpretation of the onset of irreversibility. We then unveil a
quantitative relation between the entropy production rate and correlations,
both total and quantum, built between the two oscillators. In the
small-coupling limit, the entropy production rate is shown to be proportional
to both the mutual information and the quantum correlations. We apply our
results to the analysis of the optomechanical interaction between a
nano-mechanical resonator and a cavity field, and show that the behavior of the
entropy production captures the peculiar features of the model, such as
sideband cooling and amplification.
