  We use the Chapman-Enskog method to derive the Smoluchowski equation from the
Kramers equation in a high friction limit. We consider two main extensions of
this problem: we take into account a uniform rotation of the background medium
and we consider a generalized class of Kramers equations associated with
generalized free energy functionals. We mention applications of these results
to systems with long-range interactions (self-gravitating systems, 2D vortices,
bacterial populations,...). In that case, the Smoluchowski equation is
non-local. In the limit of short-range interactions, it reduces to a
generalized form of the Cahn-Hilliard equation. These equations are associated
with an effective generalized thermodynamical formalism.
