The information theory approach is used to study molecular-scale density fluctuations and solvation of hard-core molecules in a condensed polymeric system, supported by extensive computer simulations. In contrast to simple liquids, it is found that the bond connectivity in polymers leads to non-Gaussian density fluctuations in molecular volumes. We define "renormalized" polymers with a reduced number of monomers of increased effective size. This reduces correlations between monomers and simplifies the effective density fluctuations. Chemical potentials of hard-core solutes in polyethylene can then be calculated accurately using information theory.