  After reviewing the main properties of time-evolutions of open quantum
systems, some considerations about the positivity of factorized Markovian
dynamics for bipartite systems are made. In particular, it is shown that the
positivity of the whole time-evolution in general does not ask for the complete
positivity of the single system time-evolutions, if they are allowed to differ.
However, they must be completely positive if one is a small perturbation of the
other, which is the typical situation for open systems in a heat bath.

Quantum Physics