Thermal corrections in the Casimir interaction between a metal and dielectric

The Casimir interaction between two thick parallel plates, one made of metal and the other of a dielectric, is investigated at nonzero temperature. It is shown that in some temperature intervals the Casimir pressure and the free energy of a fluctuating field are nonmonotonic functions of temperature and the corresponding Casimir entropy can be negative. A physical interpretation for these conclusions is given. At the same time we demonstrate that the entropy vanishes when the temperature goes to zero, i.e., in the Casimir interaction between a metal and a dielectric the Nernst heat theorem is satisfied. The investigation is performed both analytically, by using the model of an ideal metal and dilute dielectric or dielectric with a frequency-independent dielectric permittivity, and numerically for a real metal (Au) and dielectrics with different behaviors of the dielectric permittivity along the imaginary frequency axis (Si and alpha-Al2O3).