Markovian equations of motion for non-Markovian coarse-graining and properties for graphene blobs

We obtain Markovian equations of motion for a many body system of interacting coarse-grained (CG) variables and additional fluxes. The investigated CG variables belong to the special family of linear combinations of atomistic degrees of freedom. The system of Markovian equations of motion approximates Mori's exact non-Markovian generalized Langevin equation and is easy to solve by computer simulation. All parameters of the equations can be obtained from equilibrium molecular dynamics simulations of the investigated microscopic system. These parameters are either equal to the famous static covariances from Mori's continued fraction or they represent generalized constant friction matrices. We propose two different ways to compute these friction matrices based on Mori's continued fraction. Finally, some of the parameters are computed numerically for the special case of centre of mass variables in the graphene lattice and it is found that the CG variables interact with their additional fluxes in a spatially very local way.