Journal of Statistical Physics, Vol. 110, Nos. 3–6, March 2003, p. 1039-1054.
We present an overview of recent research applying ideas of statistical mechanics to try to better understand the statics and especially the dynamic puzzles regarding liquid water. We discuss recent molecular dynamics simulations using the Mahoney-Jorgensen transferable intermolecular potential with five points (TIP5P), which is closer to real water than previously-proposed classical pairwise additive potentials. Simulations of the TIP5P model for a wide range of deeply supercooled states, including both positive and negative pressures, reveal (i) the existence of a non-monotonic temperature of maximum density line and a non-reentrant spinodal, (ii) the presence of a low-temperature phase transition. The take-home message for the static aspects is that what seems to "matter" more than previously appreciated is local tetrahedral order, so that liquid water has features in common with SiO2 and P, as well as perhaps Si and C. To better understand dynamic aspects of water, we focus on the role of the number of diffusive directions in the potential energy landscape. What seems to "matter" most is not values of thermodynamic parameters such as temperature T and pressure P, but only the value of a parameter characterizing the potential energy landscape—just as near a critical point what matters is not the values of T and P but rather the values of the correlation length.