Repulsive Casimir–Lifshitz pressure in closed cavities

We consider the interaction pressure acting on the surface of a dielectric sphere enclosed within a magnetodielectric cavity. We determine the sign of this quantity regardless of the geometry of the cavity for systems at thermal equilibrium, extending the Dzyaloshinskii–Lifshitz–Pitaevskii result for homogeneous slabs. As in previous theorems regarding Casimir–Lifshitz forces, the result is based on the scattering formalism. In this case, the proof follows from the variable phase approach of electromagnetic scattering. With this, we present configurations in which both the interaction and the self-energy contribution to the pressure tend to expand the sphere.