Statistical Mechanical Paradigms for Next-Generation Multiscale Theory and Simulation

Nature is intrinsically multiscale, with physical length scales ranging from the Planck length to planetary scales. Since these processes span a wide range of spatiotemporal scales, a highly successful "multiscale" model is required to deliver a consistent description across different length and time scales. Molecular soft matter is an important but challenging system for implementing a multiscale approach, since the properties arising from chemical or physical changes take place on the femto to exascales, ranging over 30 orders of magnitude. This thesis focuses on developing new paradigms for understanding the principles of statistical mechanics underlying multiscale modeling and for faithful construction of multiscale models of molecular soft matter. This thesis will systematically approach the multiscale challenge from three first-principles-based perspectives: design principles, model universality, and model fidelity. The results presented here demonstrate that rigorous, physics-driven coarse-grained modeling can facilitate the efficient simulation of complex molecular soft matter and can guide a future era of multiscale modeling.