The influence of the inclusion of a silica nanoparticle on the spatial distribution of the local stresses and the locally resolved excess Helmholtz free energy of sorption of small penetrants (He, H-2, O-2, and CO2) in a polystyrene matrix is studied by molecular dynamics simulations. The local deviations of these quantities from their bulk averages are correlated with spatial peculiarities in structural and dynamical properties, for instance in the mass density, the segmental orientation, and the mean-square atomic positional fluctuations in the polymer matrix. Relative to the bulk, stress anisotropies are slightly enhanced in the neighborhood of a nanoparticle. This is demonstrated by the spatial variations of the local shear stress and the local von Mises shear stress. For all penetrants considered, the region near the interphase is found to be a preferential sorption site. The two stress estimators are compared against one of the most frequently adopted descriptors, i.e., the radial mass density distribution. We show that the estimated interphase width depends on the quantity considered. The interphase width based on variations of the local stresses is considerably shorter than the estimate obtained using the mass density distribution. Furthermore, we find that the interphase width derived from the locally resolved Helmholtz free energy strongly depends on the size of the inserted molecule. For the smallest particle, the helium atom, a broader interphase is found than for the larger molecular species. In the case of carbon dioxide insertion, we estimate an extension similar to the one derived by stress profiles. By artificially reducing the interactions between the nanoparticle atoms and those of the polymer matrix, an attempt has been made to identify links between different ways to define the interphase thickness. It is shown that the quantities under consideration lead to interphase widths which are independent of each other.