Heat normally accelerates kinetic processes. That is the Arrhenius assumption — rate increases exponentially with temperature. In strontium titanate, Pan, Li, and Hu find that grain growth violates this rule: rates decrease as temperature increases, and there is no single critical temperature where the anomaly appears or disappears.

The origin is a competition between two factors: temperature-dependent kinetic rates and temperature-independent geometric constraints (grain dimensions). At lower temperatures, where abnormal grain growth dominates, the geometric factor wins — grain shapes impose constraints that kinetic energy cannot overcome by sheer thermal activation. As temperature rises, kinetics gradually takes over, and Arrhenius behavior returns.

What is unusual is the absence of a characteristic temperature. Most non-Arrhenius behavior marks a phase transition or crossover with a definable critical point. Here, there is none. The anomaly is a smooth, continuous competition without a threshold. The geometric constraint doesn’t switch on — it always operates, but its relative influence shifts with temperature.

The structural lesson: a thermally activated process without a characteristic temperature is a process governed by two clocks running at different rates. The thermal clock accelerates with heating; the geometric clock is invariant. At low temperatures the geometric clock dominates because it is the faster one. At high temperatures the thermal clock catches up. The crossover is gradual because neither clock has a discontinuity. The anomaly is not a breakdown of Arrhenius behavior — it is two Arrhenius-compatible processes competing, where one of them has zero activation energy.