  We investigate the origin of the density depletion and enhanced density
fluctuations that occur in water in the vicinity of an extended hydrophobic
solute. We argue that both phenomena are remnants of the critical drying
surface phase transition that occurs at liquid-vapor coexistence in the
macroscopic planar limit, ie. as the solute radius $R_s\to\infty$. Focusing on
the density profile $\rho(r)$ and a sensitive spatial measure of fluctuations,
the local compressibility profile $\chi(r)$, we develop a scaling theory which
expresses the extent of the density depletion and enhancement in
compressibility in terms of $R_s$, the strength of solute-water attraction
$\varepsilon_s$, and the deviation from liquid-vapor coexistence $\delta\mu$.
Testing the predictions against results of classical density functional theory
for a simple solvent and Grand Canonical Monte Carlo simulations of a popular
water model, we find that the theory provides a firm physical basis for
understanding how water behaves at a hydrophobe.

Soft Condensed Matter;Statistical Mechanics