We investigate the modeling of a polymer melt on large length scale by aver
aging out fast fluctuating degrees of freedom in the microscopic model. We
determine pair interactions in the coarse-grained system that give the best
representation of the fine-grained system in a variational sense. Starting
from the Gibbs-Bogoliubov inequality we derive a correction to a trial pot
ential that minimizes the variational free energy of the coarse-grained sys
tem. By applying this correction repeatedly, pair interactions that are opt
imal in variational sense are obtained self-consistently. To calculate the
potential of mean force in the polymer system, we consult the replica appro
ach. The effective potential results in a radial distribution function for
the coarse-grained sites that is less structured than that of the microscop
ic system. We also found that the soft effective interaction is unable to r
eproduce the virial distribution of the fine-grained system. (C) 2001 Ameri
can Institute of Physics.