The structural glass transition and the entropy of the metastable states

The metastable states of a glass are counted by adding a weak pinning field which explicitly breaks the ergodicity. Their entropy, that is the logarithm of their number, is extensive in a range of temperatures $T_G < T < T_C$ only, where $T_G$ and $T_C$ correspond to the ideal calorimetric and kinetic glass transition temperatures respectively. An explicit self-consistent computation of the metastable states entropy for a non disordered model is given.