  The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows one to
treat a molecular system with different levels of resolution depending on the
location of the molecules. The construction of a Hamiltonian based on the this
idea (H-AdResS) allows one to formulate the usual tools of ensembles and
statistical mechanics. We present a number of exact and approximate results
that provide a statistical mechanics foundation for this simulation method. We
also present simulation results that illustrate the theory.
