  We show how reaction coordinate path lengths affect the relaxation efficiency
of a complex system. To this purpose, we consider the metric contributions to
the transition rates. These metric contributions preserve informations about
the geometry change of the system at the barrier crossing and, therefore, are
directly related to the path lengths. The output of the present work can lead
to identify a way to enrich our knowledge about the ability of the complex
systems to relax only to preferential structures.
