Structural Glass Transition and the Entropy of the Metastable States

The metastable states of a glass are localized and counted by adding a weak pinning field that explicitly breaks the ergodicity. The entropy of the metastable states, that is, the logarithm of their number, is extensive in a range of temperatures $T_s<T<\mathrm{}{T}_c$ only. It is argued that $T_s$ and $T_c$ are the ideal calorimetric and kinetic transition temperatures, respectively. An explicit computation of the metastable states entropy for a $({\overrightarrow{\phi }}^2{)}^2$ model is given.