Mesoscopic MCT theory resolves Giant Non-Gaussian Parameter and Flory's conjecture

Abstract

Extending Prigogine's ideas to the interior of the system, we generalize mode-coupling theory from a microscopic to a mesoscopic formulation by incorporating the non-equilibrium eigen-phase. The resulting framework resolves two long-standing puzzles in glass transition physics with an error less than 0.01 against experiments: (i) the giant non-Gaussian parameter $\alpha_{2} \sim 1-10$ which exceeds standard MCT predictions (only 0.1) by two orders of magnitude; (ii) the universal WLF constant $C_{1}=17 \ln 10 /(3 \sqrt{42}-19) \approx 16.7$, empirically observed for seven decades but never derived from first principles(e.g. Adam-Gibbs $C_{1}=8.5$, while other theories are off by more than a factor of two). These results establish mesoscopic MCT as a measurable foundation for non-equilibrium thermodynamics, unifying dynamic heterogeneity and thermodynamic universality in glass-forming systems.