Redfield reduced dynamics and entanglement

In phenomenological applications, the time evolution of subsystems immersed in an external environment is sometimes described by Markovian semigroups of the Redfield type that have non-positive results: the appearance of negative probabilities is avoided by restricting the admissible initial conditions to those states that remain positive under the action of the dynamics. We show that this often adopted procedure may lead to physical inconsistencies in the presence of entanglement