  Simulations of water near extended hydrophobic spherical solutes have
revealed the presence of a region of depleted density and accompanying enhanced
density fluctuations.The physical origin of both phenomena has remained
somewhat obscure. We investigate these effects employing a mesoscopic binding
potential analysis, classical density functional theory (DFT) calculations for
a simple Lennard-Jones (LJ) solvent and Grand Canonical Monte Carlo (GCMC)
simulations of a monatomic water (mw) model. We argue that the density
depletion and enhanced fluctuations are near-critical phenomena. Specifically,
we show that they can be viewed as remnants of the critical drying surface
phase transition that occurs at bulk liquid-vapor coexistence in the
macroscopic planar limit, i.e.~as the solute radius $R_s\to\infty$. Focusing on
the radial density profile $\rho(r)$ and a sensitive spatial measure of
fluctuations, the local compressibility profile $\chi(r)$, our binding
potential analysis provides explicit predictions for the manner in which the
key features of $\rho(r)$ and $\chi(r)$ scale with $R_s$, the strength of
solute-water attraction $\varepsilon_{sf}$, and the deviation from liquid-vapor
coexistence of the chemical potential, $\delta\mu$. These scaling predictions
are confirmed by our DFT calculations and GCMC simulations. As such our theory
provides a firm basis for understanding the physics of hydrophobic solvation.
