  Many features of a molecule which are of physical interest (e.g. molecular
conformations, reaction rates) are described in terms of its dynamics in
configuration space. This article deals with the projection of molecular
dynamics in phase space onto configuration space. Specifically, we study the
situation that the phase space dynamics is governed by a stochastic Langevin
equation and study its relation with the configurational Smoluchowski equation
in the three different scaling regimes: Firstly, the Smoluchowski equations in
non-Cartesian geometries are derived from the overdamped limit of the Langevin
equation. Secondly, transfer operator methods are used to describe the
metastable behaviour of the system at hand, and an explicit small-time
asymptotics is derived on which the Smoluchowski equation turns out to govern
the dynamics of the position coordinate (without any assumptions on the
damping). By using an adequate reduction technique, these considerations are
then extended to one-dimensional reaction coordinates. Thirdly, we sketch three
different approaches to approximate the metastable dynamics based on time-local
information only.
