Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship

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.

Automated summary

The ultimate goal of this series of articles is to establish a better correspondence between the dynamics of fine-grained (FG) and coarse-grained (CG) models. By utilizing the excess entropy scaling relationship, the authors show that FG and CG counterparts follow the same universal scaling relationship. They develop a new theory to calculate excess entropies for both FG and CG systems, taking into account entropy representability. Applying the excess entropy scaling idea to liquid water and methanol systems, they find that the scaling exponents remain unchanged during the coarse-graining process, indicating universality of the scaling behavior for the same underlying molecular systems. Furthermore, they demonstrate that missing entropy plays a crucial role in accelerating CG dynamics.