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The coarse-grained modeling of molecular systems is a burgeoning field, yet significant chal- lenges remain in interpreting these models and understanding how to build new ones for new systems. Bottom-up coarse-graining provides methodology for building new coarse-grained models systematically and theoretical foundations for understanding how to interpret coarse- grained models more generally. However, it has limitations, especially when it comes to mod- eling systems of complex molecules. This thesis describes research that begins with work towards deeper understanding of the bottom-up coarse-graining of many relatively simple molecules, then branches towards work on the coarse-graining of few complex molecules, and finally concludes by pursuing work on the coarse-graining of many moderately complex molecules. The results of these threads are 1) new theory of coarse-grained equilibrium thermodynamics with powerful tools for its computational investigation, 2) deep theoretical insight into nonequilibrium adaptation, proven by a flurry of methodological applications in enhanced sampling, and 3) expanded paradigms for the renormalization of complex molecular systems that provide foundations for otherwise impossible modeling challenges.


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