  Coarse-graining is central to reducing dimensionality in molecular dynamics,
and is typically characterized by a mapping which projects the full state of
the system to a smaller class of variables. While extensive literature has been
devoted to coarse-graining starting from reversible systems, not much is known
in the non-reversible setting. In this article, starting with a non-reversible
dynamics, we introduce and study an effective dynamics which approximates the
(non-closed) projected dynamics. Under fairly weak conditions on the system, we
prove error bounds on the trajectorial error between the projected and the
effective dynamics. In addition to extending existing results to the
non-reversible setting, our error estimates also indicate that the notion of
mean force motivated by this effective dynamics is a good one.
