Relaxation to equilibrium driven via indirect control in Markovian dynamics

We characterize to what extent it is possible to modify the stationary states of a quantum dynamical semigroup, that describes the irreversible evolution of a two-level system, by means of an auxiliary two-level system. We consider systems that can be initially entangled or uncorrelated. We find that the indirect control of the stationary states is possible, even if there are not initial correlations, under suitable conditions on the dynamical parameters characterizing the evolution of the joint system.