Avoiding the Kauzmann Paradox via Interface-Driven Divergence in States

Kauzmann paradox (KP) suggests that deeply supercooled liquids can have a lower entropy than the corresponding crystalline solids. While this entropy catastrophe has been thoroughly studied via equilibrium thermodynamics, the solidification process occurs far-from-equilibrium. By analyzing this process experimentally and theoretically, we show that surface chemical speciation (oxidation-driven generation and self-organization of different species of the alloy components) in core-shell particles (CSPs) can perturb the entropy production to an extent that a continuum equilibrium phase transition is not possible. Speciation of the surface causes divergence of associated stress vectors that generate nonequilibrium fluxes and frustrates homogeneous nucleation hence deep undercooling. The asymmetry of the speciation-derived surface tensor skews the minimum entropy production criterion. We analyze a set of nonequilibrium models, one showing and one averting the entropy catastrophe. Applying thermodynamic speed limits to these models, we show that the KP takes another form. Deviations from the speed limit diverge the configurational entropy of the glass, but adding an interfacial state avoids the entropy catastrophe with significantly large supercooling.