A tetrahedral entropy for water

We introduce the space-dependent correlation function C-Q(r) and time-dependent autocorrelation function C-Q(t) of the local tetrahedral order parameter Q Q(r, t). By using computer simulations of 512 waterlike particles interacting through the transferable interaction potential with five points (TIP5 potential), we investigate C-Q(r) in a broad region of the phase diagram. We find that at low temperatures C-Q(t) exhibits a two-step time-dependent decay similar to the self-intermediate scattering function and that the corresponding correlation time tau(Q) displays a dynamic cross-over from non-Arrhenius behavior for T > T-W to Arrhenius behavior for T < T-W, where T-W denotes the Widom temperature where the correlation length has a maximum as T is decreased along a constant-pressure path. We define a tetrahedral entropy S-Q associated with the local tetrahedral order of water molecules and find that it produces a major contribution to the specific heat maximum at the Widom line. Finally, we show that tau(Q) can be extracted from S-Q by using an analog of the Adam-Gibbs relation.