About non-positive evolutions in open system dynamics

The long-time evolution of a system in interaction with an external environment is usually described by a family of linear maps g_t, generated by master equations of Block-Redfield type. These maps are in general non-positive; a widely adopted cure for this physical inconsistency is to restrict the domain of definition of the dynamical maps to those states for which g_t remains positive. We show that this prescription has to be modified when two systems are immersed in the same environment and evolve with the factorized dynamics g_t x g_t starting from an entangled initial state.