A novel type of a multiscale approach, called Relative
Resolution
(RelRes), can correctly retrieve the behavior of various nonpolar
liquids while speeding up molecular simulations by almost an order
of magnitude. In this approach in a single system, molecules switch
their resolution in terms of their relative separation, with near
neighbors interacting via fine-grained potentials, yet far neighbors
interacting via coarse-grained potentials; notably, these two potentials
are analytically parametrized by a multipole approximation. Our current
work focuses on analyzing RelRes by relating it with the Kullback–Leibler
(KL) entropy, which is a useful metric for multiscale errors. In particular,
we thoroughly examine the exact and approximate versions of this informatic
measure for several alkane systems. By analyzing its dependency on
the system size, we devise a formula for predicting the exact KL entropy
of an “infinite” system via the computation of the approximate
KL entropy of an “infinitesimal” system. Demonstrating
that the KL entropy can holistically capture many multiscale errors,
we settle bounds for the KL entropy that ensure a sufficient representation
of the structural and thermal behavior by the RelRes algorithm. This,
in turn, allows the scientific community to readily determine the
ideal switching distance for an arbitrary RelRes system.