Fig. 1.

Density fluctuations within a cubic probe volume, of size 12 Å $\times$ 12 Å $\times$ 12 Å, in bulk liquid water. (A) Cross-sectional snapshot from an atomistic MD simulation, showing the probe volume v in blue. (B and C) Probability distribution $P_v\left(N\right)$ of the number of water molecules whose center lies in v. Results are shown for atomistic simulations, for the LCW-inspired coarse-grained model of Eq. 5, for the conventional lattice gas of Eq. 1, and for the continuum estimate of Eq. 9. Lattice models were simulated with two parameter sets consistent with the macroscopic surface tension of the air–water interface. The lower temperature case $(T<T_{\text{R}}$ parameters, $\mathit{ϵ}/T=6,$ $\delta =4$ Å) does not support capillary fluctuations. The $T>T_{\text{R}}$ parameters $(\mathit{ϵ}/T=1.35$, $\delta =1.84$ Å), by contrast, describe an interface whose shape fluctuations are consistent with capillary wave theory. Results for Eq. 5 with the $T<T_{\text{R}}$ parameters, plotted in B, data from ref. 13.