Kauzmann Paradox: a crossover due to diminishing local excitations

Abstract

The configurational entropy of supercooled liquids extrapolates to zero at the Kauzmann temperature, causing a crisis called the Kauzmann paradox. Here, using a class of multicomponent lattice glass models, we study a resolution of the paradox characterized by a sudden but smooth turn in the entropy as temperature goes sufficiently low. A scalar variant of the models reproduces the Kauzmann paradox with thermodynamic properties at very low temperatures dominated by correlations. An exactly solvable vector variant without correlation illustrates that a sudden entropy turn occurs when discrete local excitations are largely suppressed. Despite being disordered and infinitely degenerate, the ground states have zero entropy per particle.