  The elastic deformation of a soft solid induced by capillary forces crucially
relies on the excess stress inside the solid-liquid interface. While for a
liquid-liquid interface this "surface stress" is strictly identical to the
"surface free energy", the thermodynamic Shuttleworth equation implies that
this is no longer the case when one of the phases is elastic. Here we develop a
microscopic model that incorporates enthalpic interactions and entropic
elasticity, based on which we explicitly compute the surface stress and surface
free energy. It is found that the compressibility of the interfacial region,
through the Poisson ratio near the interface, determines the difference between
surface stress and surface energy. We highlight the consequence of this finding
by comparing with recent experiments and simulations on partially wetted soft
substrates.
