| The main focus of this thesis is the relation between the liquid-liquid phase transition and thermodynamics and dynamic anomalies. The Jagla model of a liquid, which consists of particles interacting via a spherically-symmetric two-scale potential with both repulsive and attractive ramps, is studied via molecular dynamics simulations. This potential displays anomalies similar to those found in liquid water, namely expansion upon cooling and an increase of diffusivity upon compression, as well as a liquid-liquid (LL) phase transition in the region of the phase diagram accessible to simulations. The LL coexistence line, unlike in tetrahedrally-coordinated liquids, has a positive slope, because of the Clapeyron relation, corresponding to the fact that the high density phase (HDL) is more ordered than low density phase (LDL). When the system at constant pressure above the critical pressure is cooled, its thermodynamic properties rapidly change from LDL-like to HDL-like upon crossing the Widom line. The temperature dependence of the diffusivity also changes rapidly in the vicinity of the Widom line emanated from the LL critical point. This finding provides a possible explanation for the dynamic crossover observed in water.; The phenomenology associated with the glass transition is also studied by cooling the liquid to the glass state and heating the glass back to the liquid phase. It is found that, at high pressure, the heat capacity shows two maxima upon heating the glass, with one at high temperature associated with the Widom line, and the other at low temperature linked to the kinetically arrested glass state. At low pressure, the effect of the glass transition on the density minimum is observed, as well as the effect of crystallization on the glass transition. The findings are mapped to the case of water and provide a possible picture for water's glass transition in the context of the hypothesized liquid-liquid phase transition.; Finally, the Stokes-Einstein relation and the relative populations of LDL-like and HDL-like local structures of TIP5P water and Jagla liquid are investigated. The results, consistent with the experimental results of confined water for nanogeometrics in a wide range of temperature at ambient pressure, show that the breakdown of Stokes-Einstein relation coincides with the temperature at which the relative population of the particles with no neighbors starts to increase rapidly. Thus, the study suggests that the Stokes-Einstein relation breakdown is related to the inhomogeneity of local structures, indicated by the relative population change of the LDL and the HDL local structures. |
