  We investigate the dynamics of the driven open double two-level system by
deriving a driven Markovian master equation based on the Lewis-Riesenfeld
invariant theory. The transitions induced by coupling to the heat reservoir
occur between the instantaneous eigenstates of the Lewis-Riesenfeld invariant.
Therefore, different driving protocols associated with corresponding
Lewis-Riesenfeld invariants result in different open system dynamics and
symmetries. In particular, we show that since the instantaneous steady state of
the driven double two-level system is one of eigenstates of the
Lewis-Riesenfeld invariant at ultralow reservoir temperature, the inverse
engineering method based on the Lewis-Riesenfeld invariants has a good
performance in rapidly preparing the quantum state of open quantum systems. As
an example, a perfect entangled state is generated by means of the inverse
engineering method.
