  An undercooled liquid is unstable. The driving force of the glass transition
at Tg is a change of the undercooled-liquid Gibbs free energy. The classical
Gibbs free energy change for a crystal formation is completed including an
enthalpy saving. The crystal growth critical nucleus is used as a probe to
observe the Laplace pressure change Dp accompanying the enthalpy change -Vm *Dp
at Tg where Vm is the molar volume. A stable glass-liquid transition model
predicts the specific heat jump of fragile liquids at temperatures smaller than
Tg, the Kauzmann temperature TK where the liquid entropy excess with regard to
crystal goes to zero, the equilibrium enthalpy between TK and Tg, the maximum
nucleation rate at TK of superclusters containing magic atom numbers, and the
equilibrium latent heats at Tg and TK. Strong-to-fragile and strong-to-strong
liquid transitions at Tg are also described and all their thermodynamic
parameters are determined from their specific heat jumps. The existence of
fragile liquids quenched in the amorphous state, which do not undergo
liquid-liquid transition during heating preceding their crystallization, is
predicted. Long ageing times leading to the formation at TK of a stable glass
composed of superclusters containing up to 147 atoms, touching and
interpenetrating, are evaluated from nucleation rates. A fragile-to-fragile
liquid transition occurs at Tg without stable-glass formation while a strong
glass is stable after transition.
