  Measurements of local density fluctuations are crucial to characterizing the
interfacial properties of equilibrium fluids. A specific case that has been
well-explored involves the heightened compressibility of water near hydrophobic
entities. Commonly, a spatial profile of local fluctuation strength is
constructed from measurements of the mean and variance of solvent particle
number fluctuations in a set of contiguous sub-volumes of the system adjacent
to the solvo/hydrophobe. An alternative measure proposed by Evans and Stewart
(J. Phys.: Condens. Matter 27, 194111 (2015)) defines a local compressibility
profile in terms of the chemical potential derivative of the spatial number
density profile. Using Grand Canonical Monte Carlo simulation, we compare and
contrast the efficacy of these two approaches for a Lennard-Jones solvent at
spherical and planar solvophobic interfaces, and SPC/E water at a hydrophobic
spherical solute. Our principal findings are that: (i) the local
compressibility profile $\chi({\bf r})$ of Evans and Stewart is considerably
more sensitive to variations in the strength of local density fluctuations than
the spatial fluctuation profile $F({\bf r})$ and can resolve much more detailed
structure; (ii) while the local compressibility profile is essentially
independent of the choice of spatial discretization used to construct the
profile, the spatial fluctuation profile exhibits strong systematic dependence
on the size of the subvolumes on which the profile is defined. We clarify the
origin and nature of this finite-size effect.
