Glass transition and entropy: Kauzmann's paradox

After melting, the entropy of a liquid is higher than that of the crystal. Since the C _p (C _p = T ∂S / ∂T) of a liquid is higher than that of the crystal, the entropy S of the liquid decreases faster than that of the crystal. For brittle liquids, the entropy difference between liquid and crystal decreases by around a factor of 3 between T _m and T _g . For most glass formers, especially molecular compounds, extrapolation below T _g of the entropy evolution S (T), measured at higher temperatures, leads to a virtual crossover with the crystal entropy at a positive temperature T _K (Kauzmann temperature