Dynamics of an inhomogeneously coarse grained multiscale system

To study material phenomena simultaneously at various length scales, descriptions in which matter can be coarse grained to arbitrary levels are necessary. Attempts to do this in the static regime (i.e., zero temperature) have already been developed. We present an approach that leads to a dynamics for such coarse grained models. This allows us to obtain temperature-dependent and transport properties. Renormalization group theory is used to create new local potential models between nodes, within the approximation of local thermodynamical equilibrium. Assuming that these potentials give an average description of node dynamics, we calculate thermal and mechanical properties. If this method can be sufficiently generalized it may form the basis of a multiscale molecular dynamics method with time and spatial coarse graining.