Effective equations for reaction coordinates in polymer transport

Abstract: 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.