In general, entropy comes from the degrees of freedom in momenta and positions of nuclei and electrons. More specifically, most of the entropy comes from vibrations of atoms. The usual interest is in differences of entropy between different states of a material, however, and the configurations of atoms and spins can also make important contributions to differences in entropy.
For materials, entropy plays its biggest role at high temperatures. The new features at high temperatures are the strong couplings between different degrees of freedom. The interactions: phonon-phonon, electron-phonon, magnon-phonon, can all be important for the entropy and free energy. Sorting out these couplings requires analysis of the underlying mechanisms, and I will show some examples with Pd, Si, and FeTi that I hope you find interesting.