  The description of the dynamics of a complex, high-dimensional system in
terms of a low-dimensional set of collective variables Y can be fruitful if the
low dimensional representation satisfies a Langevin equation with drift and
diffusion coefficients which depend only on Y. We present a computational
scheme to evaluate whether a given collective variable provides a faithful
low-dimensional representation of the dynamics of a high-dimensional system.
The scheme is based on the framework of finite-difference Langevin-equation,
similar to that used for molecular-dynamics simulations. This allows one to
calculate the drift and diffusion coefficients in any point of the
full-dimensional system. The width of the distribution of drift and diffusion
coefficients in an ensemble of microscopic points at the same value of Y
indicates to which extent the dynamics of Y is described by a simple Langevin
equation. Using a simple protein model we show that collective variables often
used to describe biopolymers display a non-negligible width both in the drift
and in the diffusion coefficients. We also show that the associated effective
force is compatible with the equilibrium free--energy calculated from a
microscopic sampling, but results in markedly different dynamical properties.
