A kinetic criterion for Stokes–Einstein relation breakdown based on effective collisional geometry

We propose a kinetic framework for interpreting the Stokes–Einstein (SE) relation breakdown in supercooled liquids by introducing an effective collision diameter, d_eff, derived from transport data. Numerical simulations of a model CuZr alloy reveal that d_eff increases upon cooling but saturates near the first peak of the radial distribution function just before SE breakdown. This saturation defines a geometric upper bound for the collisional cross-section beyond which further slowdown is governed by cooperative, heterogeneous motion rather than local collisional transport. Our analysis yields a compact criterion for SE breakdown in a mean-field perspective and provides physically interpretable inputs for future data-driven models of glassy dynamics.