  In the framework of the problem of finding proper reaction coordinates (RCs)
for complex systems and their effective evolution equations, we consider the
case study of a polymer chain in an external double-well potential,
experiencing thermally activated dynamics. Langevin effective equations
describing the macroscopic dynamics of the system can be inferred from data by
using a data-driven approach, once a suitable set of RCs is chosen. We show
that, in this case, the validity of such choice depends on the stiffness of the
polymer's bonds: if they are sufficiently rigid, we can employ a reduced
description based only on the coordinate of the center of mass; whereas, if the
stiffness reduces, the one-variable dynamics is no more Markovian and (at
least) a second reaction coordinate has to be taken into account to achieve a
realistic dynamical description in terms of memoryless Langevin equations.
