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.
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