  We provide a general discussion of the Liouvillian spectrum for a system
coupled to a non-Markovian bath using Floquet theory. This approach is suitable
when the system is described by a time-convolutionless master equation with
time-periodic rates. Surprisingly, the periodic nature of rates allow us to
have a stroboscopic divisible dynamical map at discrete times, which we refer
to as Floquet stroboscopic divisibility. We illustrate the general theory for a
Schr\"odinger cat which is roaming inside a non-Markovian bath, and demonstrate
the appearance of stroboscopic revival of the cat at later time after its
death. Our theory may have profound implications in entropy production in
non-equilibrium systems.
