Irreversibility and correlations in coupled quantum oscillators

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.