Are defect models consistent with the entropy and specific heat of glass-formers?

We show that point-like defect model of glasses cannot explain thermodynamic properties of glass-formers, as for example the excess specific heat close to the glass transition, contrary to the claim of J.P. Garrahan, D. Chandler [Proc. Natl. Acad. Sci. 100, 9710 (2003)]. More general models and approaches in terms of extended defects are also discussed.