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The problem of estimating the thermal corrections to Casimir andCasimir-Polder interactions in systems involving conducting plates hasattracted considerable attention in the recent literature on dispersion forces.Alternative theoretical models, based on distinct low-frequency extrapolationsof the plates reflection coefficient for transverse electric (TE) modes,provide widely different predictions for the magnitude of this correction. Inthis paper we examine the most widely used prescriptions for this reflectioncoefficient from the point of view of their consistency with the Bohr-vanLeeuwen theorem of classical statistical physics, stating that at thermalequilibrium transverse electromagnetic fields decouple from matter in theclassical limit. We find that the theorem is satisfied if and only if the TEreflection coefficient vanishes at zero frequency in the classical limit. Thiscriterion appears to rule out some of the models that have been consideredrecently for describing the thermal correction to the Casimir pressure withnon-magnetic metallic plates.

Bohr-van Leeuwen theorem and the thermal Casimir effect for conductors