Abstract
On decreasing the temperature $T$, experiments on supercooled water and other network-forming liquids, such as BeF$_2$ or SiO$_2$, display a dynamic crossover from non-Arrhenius dynamics (with $T$-dependent activation energy) to Arrhenius dynamics (with constant activation energy). We show, by computer simulations and analytic results, that this dynamic behavior is related to the anomalous increase of fluctuations at low $T$. We locate the temperature of maximum fluctuation $T_W$ along the Widom line, which is expected to depart from a metastable liquid-liquid critical point. We find that $T_W$ corresponds to the maximum structural change in the liquid. We recover the dynamic crossover directly from the calculation of the free energy associated with breaking a bond and reorienting the molecule, showing that the dynamics is Arrhenius at low $T$ because of the structural change occurring at $T_W$. By analyzing the pressure-dependence of the crossover, it is possible to give insight into the mechanism ruling the physics of network-forming liquids.
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