Thermodynamics of coarse-grained models of supercooled liquids

In recent papers, we have argued that kinetically constrained coarse-grained models can be applied to understand dynamic properties of glass-forming materials, and we have used this approach in various applications that appear to validate this view. In one such paper [J. P. Garrahan and D. Chandler, Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003)], among other things we argued that this approach also explains why the heat-capacity discontinuity at the glass transition is generally larger for fragile materials than for strong materials. In the preceding article, Biroli, Bouchaud, and Tarjus have objected to our explanation on this point, arguing that the class of models we apply is inconsistent with both the absolute size and the temperature dependence of the experimental specific heat. Their argument, however, neglects parameters associated with the coarse graining. Accounting for these parameters, we show here that our treatment of dynamics is not inconsistent with heat-capacity discontinuities.