Kauzmann Paradox, Supercooling, and Finding Order in Chaos

Prediction of a liquidus state with lower entropy than the corresponding solid at Kauzmann temperature (T_k), and associated entropy catastrophe/paradox, remains an enigma. Despite efforts to resolve this paradox for nearly 80 years, no unifying resolution has been reported. Potential resolutions to the Kauzmann paradox rely on an ideal glass transition, however, this limits the interpretation of T_k as an equilibrium critical point rather than an instability. Focusing on entropy, statistical mechanics and non-equilibrium dynamics becomes a key tenet in resolving this paradox. Expansion in phase space beyond 2D and consideration of T_k as a non-equilibrium critical point is necessary to understand the extent of liquid relaxation beyond T_k. In this review, we provide an entropic perspective of the relaxation behavior of supercooled liquids, associated expanded phase diagram, and the potential resolution to the Kauzmann paradox. This work integrates the historical evolution of our understanding of entropy/thermodynamics with modern interpretation of quantum states through renormalization group and thermodynamic speed limits.