Understanding Dynamics in Coarse-Grained Models: I. Universal Excess Entropy Scaling Relationship

TL;DR

This paper demonstrates that coarse-grained models of liquids like water and methanol follow the same universal excess entropy scaling as their fine-grained counterparts, revealing the role of missing entropy in dynamics acceleration.

Contribution

It introduces a new theory to calculate excess entropies in FG and CG systems, establishing the universality of the excess entropy scaling relationship across different resolutions.

Findings

FG and CG models follow the same universal scaling relationship

Scaling exponents remain unchanged after coarse-graining

Missing entropy significantly influences CG dynamics acceleration

Abstract

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.