Abstract
The purpose of this research is to study the dynamical evolution of a system containing entangled degrees of freedom at two separated energy scales. Given a measuring device that is insensitive to the high-frequency oscillations of the high-energy quanta, we are interested in describing the observable dynamics of the low-energy subsystem, which will depend on interactions with the inaccessible degrees of freedom. To do so, we time-average the evolution equation for the reduced density matrix associated with the low-energy subsystem and find an expression for the evolution in second-order perturbation theory.