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Relationship between Structure, Entropy and Diffusivity in Water and Water-like Liquids

Anomalous behaviour of the excess entropy ($S_e$) and the associated scaling relationship with diffusivity are compared in liquids with very different underlying interactions but similar water-like anomalies: water (SPC/E and TIP3P models), tetrahedral ionic melts (SiO$_2$ and BeF$_2$) and a fluid with core-softened, two-scale ramp (2SRP) interactions. We demonstrate the presence of an excess entropy anomaly in the two water models. Using length and energy scales appropriate for onset of anomalous behaviour, the density range of the excess entropy anomaly is shown to be much narrower in water than in ionic melts or the 2SRP fluid. While the reduced diffusivities ($D^*$) conform to the excess entropy scaling relation, $D^* =A\exp (αS_e)$ for all the systems (Y. Rosenfeld, Phys. Rev. A {\bf 1977}, {\it 15}, 2545), the exponential scaling parameter, $α$, shows a small isochore-dependence in the case of water. Replacing $S_e$ by pair correlation-based approximants accentuates the isochore-dependence of the diffusivity scaling. Isochores with similar diffusivity scaling parameters are shown to have the temperature dependence of the corresponding entropic contribution. The relationship between diffusivity, excess entropy and pair correlation approximants to the excess entropy are very similar in all the tetrahedral liquids.