  A novel type of a multiscale approach, called Relative Resolution (RelRes),
can correctly retrieve the behavior of various nonpolar liquids, whilst
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 parameterized 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 for readily determining the ideal switching distance for an arbitrary
RelRes system.
