  We consider the Jaynes-Cummings model describing the interaction of a Cooper
pair box (CPB) and a nanoresonator (NR) in the presence of a Kerr medium and
losses The evolution of the entropy of both subsystems and the CPB population
inversion were calculated numerically. It is found that these properties
increase when the NR frequency is time-dependent, even in the presence of
losses; the effect is very sensitive to detuning and disappears in the resonant
regime. The roles played by the losses affecting the CPB and the NR are also
compared.
