Repulsive Casimir force at zero and finite temperature

We study the zero and finite temperature Casimir force acting on a perfectly conducting piston with arbitrary cross section moving inside a closed cylinder with infinitely permeable walls. We show that at any temperature, the Casimir force always tends to move the piston away from the walls and towards its equilibrium position. In the case of rectangular piston, exact expressions for the Casimir force are derived. In the high temperature regime, we show that the leading term of the Casimir force is linear in temperature and therefore the Casimir force has a classical limit. Due to duality, all these result also hold for an infinitely permeable piston moving inside a closed cylinder with perfectly conducting walls.