Possible resolution of the Kauzmann paradox in supercooled liquids.

Generally, the entropy of the supercooled liquid decreases more rapidly than that of the crystal. Thus, the former, if we extrapolate it smoothly below the glass-transition temperature T(g), becomes equal to the latter at the so-called Kauzmann temperature T(K). Further extrapolation below T(K) leads to the unphysical situation that the entropy of disordered liquid is lower than the ordered crystal, which results in the violation of the third law of thermodynamics. This is known as the "Kauzmann paradox" which has been the key problem of liquid-glass transition for a long time. Here we propose a simple resolution of the Kauzmann paradox by answering a fundamental question of how deeply we can supercool a liquid. We argue that the lower metastable limit T(LML), below which a liquid should crystallize before its structural relaxation, is located above the Kauzmann temperature T(K). Thus, the entropy crisis at T(K) is naturally avoided by crystallization. We suggest that it is dynamic heterogeneity that destabilizes a deeply supercooled "equilibrium" liquid state as well as a glassy state against crystallization. This may have a significant implication on the stability of a glassy state, which is of industrial importance in relation to the storage of glassy material.