Bottom-Up Coarse-Graining Bridging Various Scales: From Quantum Statistics to Mesoscale

This thesis describes a series of theoretical and computational development of bottom-up coarse-graining methods that can serve as bridges between physical models at different spatial and temporal scales. At a high resolution description, a coarse-graining theory in quantum statistics is established and shown to reproduce essential nuclear quantum effects at coarse-grained level. At a coarser molecular scale, a coarse-graining strategy involving virtual sites is developed to capture symmetrical features of underlying fine-grained structure and serve as an economic representation of many-body interactions. At mesoscale, a rigorous coarse-grained mapping between fine-grained fluids and mesoscopic models is designed and verified. The associated bottom-up coarse-graining parameterization strategy is developed to derive coarse-grained equations of motions that can be compatible with mesoscopic theories such as fluid mechanics and classical density functional theory. Finally, a field theoretic description mesoscopic models is derived with the help of hierarchical coarse-graining.