As a liquid is supercooled, the difference in entropy between the liquid and solid phase decreases. By extrapolating the heat capacity of the supercooled liquid below its glass transition temperature, it is possible to calculate the temperature at which the difference in entropies becomes zero. This temperature has been named the Kauzmann temperature.
If a liquid could be supercooled below its Kauzmann temperature, and it did indeed display a lower entropy than the crystal phase, the consequences would be paradoxical. This Kauzmann paradox has been the subject of much debate and many publications since it was first put forward by Walter Kauzmann in 1948.
One resolution of the Kauzmann paradox is to say that there must be a phase transition before the entropy of the liquid decreases. In this scenario, the transition temperature is known as the calorimetric ideal glass transition temperature T. In this view, the glass transition is not merely a kinetic effect, i.e. merely the result of fast cooling of a melt, but there is an underlying thermodynamic basis for glass formation. The glass transition temperature: