  We employ a more realistic treatment to investigate the entropy and the
excitation-inversion of a coupled system that consists of a nanomechanical
resonator and a superconducting Cooper 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.
