Analyses of coarse graining procedure for mesoscale simulation

In order to meet great progress in multi-scale modelling, one of the important issues is to know about detailed process of coarse graining. The coarse graining is a standard technique of statistical mechanics to extract specific degree(s) of freedom from a many component system. Many kinds of coarse-graining simulation methods have already been proposed. Because most of them were constructed based on a priori assumptions, making detailed analyses has been difficult from the microscopic points of view. Recently, a generalised coarse-grained (CG) equation of motion has been reported for many particle centre of mass systems straightforwardly derived from the explicit information about all the degrees of freedom at the microscopic level. This equation is mostly exact for the dynamics of CG particles defined in classical many particle systems. Therefore, making discussions about characteristics of this CG equation of motion is useful for obtaining detailed knowledge on the coarse graining from the microscopic points of view. In the present article, a review on recent discussions about characteristics of this generalised CG equation of motion is given. Previous conventional coarse-graining particle dynamics simulations can be categorised as some special cases. Generalisation, confirmation and progress of the fundamental knowledge of coarse graining are partly realised from the present discussions.