1) Even with not completely positive maps, if we can find a domain in which the action of the map is positive, why should we restrict the reduced dynamics of an open system to being exclusively completely positive? Also, what could such maps indicate physically about the system?

2) What are the arguments put forward to justify completely positive maps for describing reality? Is it always possible to decouple the system from the environment and vanish the correlation terms to ensure the evolution of the joint state to be CP (completely positive)?