The intermolecular forces that cause surface tension in multiphase systems at equilibrium give rise to pressure gradients in nonequilibrium systems. The present paper treats such systems within a framework of thermodynamics and continuum mechanics and uses a generalization of the conceptual experiment of Rowlinson and Widom which applies to systems with curved interfaces and to nonequilibrium situations where the phase interfaces are not fully developed. The pressure tensor has a component p(n) acting in the direction normal to the concentration gradient and a component p(t) acting in the plane tangent to the surface of constant concentration where p(n) - p(t) = kappa(delc)2 The concentration gradient causes an additional volumetric force not present in homogeneous fluids : dF/dV = - kappa(delc)2 (1/R1 + 1/R2) n + del(s)kappa(delc)2 Here, kappa is the gradient energy parameter appearing in the Landau-Ginzburg functional, c is the concentration of the key component, R1 and R2 are the principal radii of curvature for the surface of constant constration, n is a unit vector normal to that surface, and del(s) is the gradient along the surface. The volumetric force generates pressure gradients in systems with curved interfaces at equilibrium or can drive flow in nonequilibrium situations.