The maximum value at equilibrium of the relaxed enthalpy of some glasses is viewed as a linear function of the annealing temperature from the Kauzmann temperature TK up to a vitreous transition temperature T*g which is not time dependent. The frozen enthalpy and entropy at T*g are determined from the specific heat difference between glass and undercooled melt which is constant between TK and T*g. The Gibbs free energy change at T*g is equal to zero. The vitreous transition is a thermodynamic transition without latent heat. A model is used to describe this phenomenon. A volume energy saving εv equivalent to a complementary Laplace pressure has been added to the classical Gibbs free energy change for a crystal formation in a melt. There is a change of the Vogel–Fulcher–Tammann (VFT) temperature at T*g corresponding to a decrease of the free volume disappearance temperature. Scaling laws linking the crystal homogeneous nucleation temperatures to T*g are used to predict the two VFT temperatures, the thermodynamic vitreous transition induced by vitreous (super)-clusters and the frozen enthalpy and entropy at T*g only knowing T*g, the melting temperature Tm and the fusion heat ΔHm of any fragile glass-forming melt.