pair box. The procedure uses the Buck-Sukumar model in the microwave domain, considers the nanoresonator with a time dependent frequency and both subsystems in the presence of losses. Interesting results were found for the temporal evolutions of the entropy of each subsystem and of the excitation-inversion in the Cooper pair box. A comparison was also performed about which of these two subsystems is more sensitive to the presence of losses. The results suggest that appropriate choices of the involved time dependent parameters allow us to monitor these two features of the subsystems and may offer potential applications, e.g., in the generation of nonclassical states, quantum communication, quantum lithography.