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Relation Between the Widom line and the Strong-Fragile Dynamic Crossover in Systems with a Liquid-Liquid Phase Transition

We investigate, for two water models displaying a liquid-liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid-liquid critical point. We find a correlation between the dynamic fragility transition and the locus of specific heat maxima $C_P^{\rm max}$ (``Widom line'') emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between $C_P^{\rm max}$ and dynamic crossover is not limited to the case of water, a hydrogen bond network forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically-symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions.