| This thesis employs methods of statistical mechanics and numerical simulations to study some aspects of the thermodynamic and dynamic behavior of liquid water.;As liquid water is cooled down into the supercooled state, some regions of the sample show correlated molecular motion. Previously, only the translational motion has been the object of investigation. Given the importance of orientational dynamics for water, a question that naturally arises is whether the rotational molecular motion also shows heterogeneous dynamics. We show that the most rotationally mobile molecules tend to form clusters, "rotational heterogeneities", and we study their dependence upon observation time and temperature. Further, we show evidence that molecules belonging to dynamic heterogeneities are involved in bifurcated bonds.;Since the presence of dynamic heterogeneities is increasingly important as the temperature is lowered, one would expect a signature of this phenomenon in dynamical quantities. We study the effect of dynamic heterogeneities on the origin of the breakdown of the Stokes--- Einstein and Stokes---Einstein---Debye relations for water. These relations link the diffusivity to temperature and viscosity. We study the separation of time scales of dynamic heterogeneities and the diffusive regime. We also consider different sets of mobility, slowest and fastest, for both translational and rotational heterogeneities.;A long-standing problem in biology is the seemingly universal loss of biological activity of all biomolecules, a phenomenon termed the "protein glass transition". We explore the connection between the hypothesized liquid-liquid phase transition of water, and the protein glass transition. We find that the protein glass transition coincides with the crossing of the Widom line of hydration water.;Many different scenarios have been proposed to rationalize water's thermodynamic anomalies. We study a tell model for water using the Wolff' cluster algorithm, which permits rapid equilibration. We find that three different scenarios for the phase diagram of water can be coherently described through the concept of H bond cooperativity. Finally, we study an intriguing prediction of the tell model: the presence of two maxima in the specific heat of water. We draw connections with recent experimental data. |
