Thermal corrections in Casimir interaction between metal and dielectric

The Casimir interaction between two thick parallel plates, one made of metal and the other of 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 the nonmonotonous functions of temperature and the respective Casimir entropy can be negative. The 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 metal and 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 real metal (Au) and dielectrics with different behavior of the dielectric permittivity along the imaginary frequency axis (Si and Al_2O_3).