Fig. 4.

(A) $\beta \mathrm{\Delta }G\left(N\le N_{\text{kink}};d\right)$ is recast as $\beta \mathrm{\Delta }G\left(r;d\right)$, the free energy to form a vapor tube of radius, r. The points were obtained from the simulated free energy profiles by using the relation $\pi r^2/L^2=\left(N_{\text{liq}}-N\right)/N_{\text{liq}}$ in the region $r_{\text{kink}}<r<L/2$, and the lines are fits to macroscopic theory. (B) The portion of the free energy corresponding to the liquid basin $\left(N\ge N_{\text{kink}}\right)$ is parabolic at high N (Gaussian fluctuations), but linear at low N (fat tails in water number distributions). The crossover is gradual and occurs in the vicinity of $N_{\text{cav}}$ (square symbols), that is, the value of N for which ${\langle h_{\text{cav}}\rangle }_N$ is 0.5 with a negative slope. The linear regions have roughly the same slope for all separations.