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 identical with 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.