  We consider a free energy functional on the monomer density function that is
suitable for the study of coil-globule transition. We demonstrate, with
explicitly stated assumptions, why the entropic contribution is in the form of
the Kullback-Leibler distance, and that the energy contribution is given by
two-body and three-body terms. We then solve for the free energy analytically
on a set of trial density functions, and reproduce de Gennes' classical theory
on polymer coil-globule transition. We then discuss how our formalism can be
applied to study polymer dynamics from the perspective of dynamical density
function theory.
