Effective equations for reaction coordinates in polymer transport

TL;DR

This paper investigates how the choice of reaction coordinates affects the effective Langevin equations for polymer transport, showing that bond stiffness determines whether a single coordinate suffices or multiple are needed for accurate modeling.

Contribution

It demonstrates the dependence of reaction coordinate effectiveness on polymer bond stiffness and proposes a criterion for selecting the appropriate number of coordinates.

Findings

Rigid bonds allow a single reaction coordinate (center of mass)

Flexible bonds require multiple coordinates for accurate dynamics

Effective Langevin equations can be derived from data based on these criteria

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.