Coarse-grained equation of motion for many particle system containing internal degrees of freedom

In order to numerically investigate dynamics in large and complicated systems, it is important to derive the explicit equation of motion of an extracted tagged degree of freedom under the statistical influence of the other parts. This corresponds to adopting the procedure usually called “coarse-graining”. Up-to-now, many kinds of coarse grained (CG) simulation method have been proposed based on phenomenological equations of motion and investigated about their numerical efficiencies for practical applications. We can now investigate a dynamics of appropriate degrees of freedom, i.e., the center of mass, the orientation, the internal vibration modes, etc. of CG particles, for suitably chosen characteristics in a system. Although each of the phenomenological CG methods is well established for practical usages, it is still not sufficient to construct a multiscale simulation procedure for large and complicated systems. Some explicit relation between the coarser and finer descriptions should be grasped for deducing the CG expression based on atomistic pictures. Although Langevin equation, a typical CG equation of motion, has been derived from an atomistic equation of motion in previous literatures, most of these descriptions are limited within the equation of center-of-mass motions. In the present study, a microscopic description for arbitrarily extracted degree(s) of freedom was derived by restricting the system of CG particles constructed by tightly bounded finer particles, like polyatomic molecules. The derived equation of motion was shown to be applicable to dynamics simulation of reorientation and/or internal vibration motions of CG-particle systems by analyses of the equation for realistic conditions.