Kauzmann Paradox and Thermodynamics

A distinctive feature of low-temperature metastability and supercooling is the almost universal rapid drop in the excess entropy 

By a careful analysis, Goldstein [23] has shown that much of the excess entropy arise from nonbasin contributions, such as vibrational differences between glassy and crystalline phases, and is reflected most prominently in boson peaks. Thus, it is obvious that one cannot take the excess entropy as a genuine measure of the basin entropy or the entropy associated with the number of cell representations. 

What distinguishes experimentally prepared SCL is that the drop in its extrapolated basin entropy actually becomes negative below Tk 0 (5, 6, 9, 25]. 

It should be emphasized that there is no violation of thermodynamics just because ASex(T, V) has become negative. Although it is not very common, it is possible for SCL entropy to be less than that of the crystal. On the other hand, a negative entropy is impossible. Thus, it appears more natural to identify the Kauzmann paradox with a component of the entropy becoming negative. Accordingly, as discussed in Section 10.4.1, we interpret the Kauzmann paradox as the following entropy crisis  

Under extrapolation, a negative component of S(T, V), and not a negative Sex(T, V), signals the entropy crisis. Its implication is simply that such states cannot occur in Nature, and the onset of the crisis is gradually the underlying thermodynamic driving force for GT in molecules of all sizes. 

---