  We discuss dynamics of periodically-driven open quantum systems. The time
evolution of the quantum state is described by the quantum master equation and
the form of the dissipator is chosen so that the instantaneous stationary state
is given by the Gibbs distribution. We find that the correlation between the
population part and the coherence part of the density operator is induced by an
adiabatic gauge potential. Although the introduction of the counterdiabatic
term eliminates the correlation, additional correlations prevent a convergence
to the Gibbs distribution. We study the performance of the control by the
counterdiabatic term. The system has three different scales and the performance
strongly depends on the relations among their magnitudes.
