Correlation of energy and free energy for the thermal Casimir force between real metals

Abstract

The energy of fluctuating electromagnetic field is investigated for the thermal Casimir force acting between parallel plates made of real metal. It is proved that for nondissipative media with temperature independent dielectric permittivity the energy at nonzero temperature comprises of the (renormalized) energies of the zero-point and thermal photons. In this manner photons can be considered as collective elementary excitations of the matter of plates and electromagnetic field. If the dielectric permittivity depends on temperature the energy contains additional terms proportional to the derivatives of ε with respect to temperature, and the quasiparticle interpretation of the fluctuating field is not possible. The correlation between energy and free energy is considered. Previous calculations of the Casimir energy in the framework of the Lifshitz formula at zero temperature and optical tabulated data supplemented by the Drude model at room temperature are analysed. It is demonstrated that this quantity is not a good approximation either for the free energy or the energy. A physical interpretation of this hybrid quantity is suggested. The contradictory results in the recent literature on whether the zero-frequency term of the Lifshitz formula for the perpendicular polarized modes has any effective contribution to the physical quantities are discussed. Four main approaches to the resolution of this problem are specified. The precise expressions for entropy of the fluctuating field between plates made of real metal are obtained, which helps to decide between the different approaches. The conclusion is that the Lifshitz formula supplemented by the plasma model and the surface impedance approach are best suited to describe the thermal Casimir force between real metals.

Casimir free energy of dielectric films: classical limit, low-temperature behavior and control

“…For the nondegenerate dynamical state of lowest energy the entropy at zero temperature is equal to zero. Note that for metals with perfect crystal lattices the Lifshitz theory violates the Nernst theorem when the Drude model is used and satisfies it if the plasma model is employed [54,55,56,57,58]. For metals with impurities the Nernst heat theorem is satisfied because at very low temperature the Casimir entropy abruptly jumps to zero starting from the negative value [59].…”

Temperature dependence of the Casimir force for bulk lossy media

“…[8,9,10,11,12,13,14]). The zero-temperature contribution to the force, originating from quantum fluctuations of the electromagnetic field, is well understood.…”

Geometric origin of negative Casimir entropies: A scattering-channel analysis

“…During the last decade or so various papers have focused on the entropy related to the Casimir interactions between two solid bodies [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. An important reason for this interest lies in the fact that the Casimir entropy can reach negative values.…”