Dissipative particle dynamics for a harmonic chain: A first-principles derivation

The equations of dissipative particle dynamics for a linear harmonic chain are deduced from first principles. From the original chain, a coarse-grained chain is constructed by grouping the particles in clusters; the equations of motion for the position and momenta of these clusters are derived. The clusters interact with their neighbors with elastic springs and Brownian dashpots. We provide explicit expressions for the renormalized elastic constant, the friction coefficient, and the amplitude of the random forces.