Casimir forces out of thermal equilibrium near a superconducting transition

We present a comprehensive analysis of the out-of-equilibrium Casimir pressure between two high-[Formula: see text] superconducting plates, each kept at a different temperature. Two interaction regimes can be distinguished. While the zero-point energy dominates in the near field, thermal effects become important at large interplate separations causing a drop in the force's magnitude compared with the usual thermal-equilibrium case. Our detailed calculations highlight the competing role played by propagating and evanescent modes. Moreover, as one of the plates undergoes the superconducting transition, we predict an abrupt change in the force for any plate distance, which has not been previously observed in other systems. The sensitivity of the dielectric function of the high-[Formula: see text] superconductors makes them ideal systems for a possible direct measurement of the out-of-equilibrium Casimir pressure.