  The purpose of physics is to describe nature from elementary particles all
the way up to cosmological objects like cluster of galaxies and black holes.
Although a unified description for all this spectrum of events is desirable,
this would be highly impractical. To not get lost in unnecessary details,
effective descriptions are mandatory. Here we analyze the dynamics that may
emerge from a full quantum description when one does not have access to all the
degrees of freedom of a system. More concretely, we describe the properties of
the dynamics that arise from quantum mechanics if one has access only to a
coarse-grained description of the system. We obtain that the effective maps are
not necessarily of Kraus form, due to correlations between accessible and
nonaccessible degrees of freedom, and that the distance between two effective
states may increase under the action of the effective map. We expect our
framework to be useful for addressing questions such as the thermalization of
closed quantum systems, as well as the description of measurements in quantum
mechanics.
