Key points are not available for this paper at this time.
If the dynamics of an open quantum system 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 noninvariance of equilibrium becomes a clear sign of non-Markovianity.
Chruściński et al. (Tue,) studied this question.