Glass Viscosity Curvature from Constraint-Driven Actualization: A Physical Parity with the Vogel-Fulcher-Tammann Relation

Abstract: The Vogel-Fulcher-Tammann (VFT) equation empirically describes the super-Arrhenius viscosity of glass-forming liquids; however, its divergence at a finite temperature $T_{0}$ lacks a clear physical basis. Here, a formulation derived from Dynamic Present Theory (DP$Φ$) and its Continuous Present Actualization (CPA) framework is tested: a CPA Rate modulated by a temperature-dependent Constraint Load $C(T)$, the CPA + Constraint (CPA + C) model. This formulation was evaluated across three canonical datasets: ortho-terphenyl (OTP) measurements from Laughlin and Uhlmann (1972) and Plazek et al. (1994), and glycerol-water mixtures from Kumar et al. (1994). Across all evaluated systems, the CPA + C formulation demonstrated statistical parity with the VFT model ($R^{2} > 0.99$), reproducing the viscosity curve by more than 14 orders of magnitude. Unlike the VFT equation, this approach derives the nonlinear curvature from a physically interpretable mechanism: the increase in configurational constraint as the system approaches a CPA Lock-In threshold. These findings indicate that the residual noise observed in simpler models represents an actual physical signal, which the CPA + C model effectively isolates. This suggests that the VFT's empirical success originates from its implicit capture of an underlying constraint-driven dynamic, providing a physically interpretable foundation for one of the most enduring phenomenological equations in materials science.