Using a hybrid system (Cooper pair box plus nanomechanical resonator) in the presence of Kerr nonlinearities and losses to control the entropy of the subsystems

•The work treats a hybrid system (CPB–NR) via the Jaynes–Cummings model.•Quantum entropy and excitation–inversion are focused.•System evolution in the presence of losses is considered.

We consider the Jaynes–Cummings model to describe the interaction of a Cooper pair box and a nanomechanical resonator in the presence of a Kerr medium and losses. The evolution of the entropy of both subsystems and the Cooper pair box population inversion were calculated numerically. It was found that population inversion and entropy increase when the frequency of the nanoresonator is time-dependent, even in the presence of losses; the effect is very sensitive to detuning and disappears in resonant regime. We also compare effects of the losses on each subsystem.