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We employ a more realistic treatment to investigate the entropy and theexcitation-inversion of a coupled system that consists of a nanomechanicalresonator and a superconducting Cooper pair box. The procedure uses theBuck-Sukumar model in the microwave domain, considers the nanoresonator with atime dependent frequency and both subsystems in the presence of losses.Interesting results were found for the temporal evolutions of the entropy ofeach subsystem and of the excitation-inversion in the Cooper pair box. Acomparison was also performed about which of these two subsystems is moresensitive to the presence of losses. The results suggest that appropriatechoices of the involved time dependent parameters allow us to monitor these twofeatures of the subsystems and may offer potential applications, e.g., in thegeneration of nonclassical states, quantum communication, quantum lithography.

Controlling the nonclassical properties of a hybrid Cooper pair box system and an intensity dependent nanomechanical resonator