We have connected the dynamic fragility, namely the rapidity of the relaxation time increase upon temperature reduction, to the excess entropy and heat capacity of a large number of glass-forming polymers. The connection was obtained in a natural way from the Adam-Gibbs equation, relating the structural relaxation time to the configurational entropy. We find a clear correlation for a group of polymers. For another group of polymers, for which this correlation does not work, we emphasise the role of relaxation processes unrelated to the process in affecting macroscopic thermodynamic properties. Once an essentially temperature independent contribution of these processes is removed from the total excess entropy, the correlation between dynamic fragility and thermodynamic properties is re-established. ; Comment: 14 pages, 2 figures, 1 table. Submitted to J. Chem. Phys