  If the dynamics of an open quantum systems is non-Markovian, its {asymptotic}
state strongly depends on the initial conditions, even if the dynamics
possesses an {invariant} state. This is the very essence of memory effects. In
particular, the {asymptotic} state can remember and partially preserve its
initial entanglement. Interestingly, even if the non-Markovian evolution
relaxes to an equilibrium state, this state needs not be invariant. Therefore,
the non-invariance of equilibrium becomes a clear sign of non-Markovianity.
