Accurate coarse-grained potentials for soft matter systems: Lecture Notes

In this Chapter, we present the general statistical-mechanical theory for the derivation of effective Hamiltonians for arbitrary many-body systems in thermodynamic equilibrium. The approach towards a simplified, yet accurate,
coarse-grained view of a many-body system has proven to be particularly fruitful in the realm of the Physics of Complex Fluids, a synonym for the broad research area of Soft Matter Science, which encompasses aspects of Physics, Chemistry, Materials Science and Bioscience. After the exposition of the general formalism, we present the methods by which one can derive, in a manageable and accurate way, effective Hamiltonians for a veriety of physical systems, by exposing mutually complementary theoretical and computations techniques to this end. Further, we provide extensive exposures of specific and diverse examples from current research in soft matter systems, for which the coarse-graining approach has been applied with remarkable success.