A Constraint-Modulated Viscosity Law for Broad-Window Glass-Forming Systems

Abstract

The steep rise of viscosity as a liquid cools is one of the defining signatures of glass formation, yet the standard descriptions-Vogel-Fulcher-Tammann (VFT) and its divergence-free successors MYEGA and Avramov-Milchev-treat the slowdown as a single fixed curvature fitted across the whole temperature range. This work reports a constraint-modulated alternative built on a different premise: that a cooling liquid resolves its configuration continuously in the present, one state after another under the constraints then in force, rather than reading its viscosity off a globally predetermined free-energy surface. This premise, Continuous Present Actualization (CPA), calls for a rate law whose resolution cost changes as the liquid cools. The resulting model, CPA + Constraint (CPA + C), adds a single bounded constraint-load term C(T) that tracks how configurational access narrows toward structural lock-in. Tested against VFT, MYEGA, and Avramov-Milchev on canonical datasets for ortho-terphenyl, salol, and boron trioxide, CPA + C is favored by AIC and BIC on four of five datasets after full penalization for its two extra parameters, with margins reaching ΔAIC = 140.9 on the largest set (salol, n = 95); on two datasets the baseline kinetic term vanishes, reducing the model to four effective parameters. A smooth sigmoid form of C(T) fits equally well or better, and leave-one-out cross-validation on salol shows CPA + C generalizing to held-out data with mean prediction error three times lower than the next-best model. The single exception is the narrowest-window dataset, where the temperature range is too small for the constraint transition to separate CPA + C from simpler forms.