Equation of motion for coarse-grained simulation based on microscopic description.

We have derived an equation of motion for coarse-grained particles by using a projection operator. Because the derived coarse-grained equation is based on microscopic description, it can be the basis for models of various coarse-grained simulations. We show that by substitution of random forces into fluctuating forces in the coarse-grained equation, the equations for Brownian dynamics and dissipative particle dynamics are reproduced.