Recently, Høye, Brevik, Ellingsen, and Aarseth [Phys. Rev. E 75, 051127 (2007)] claimed that the use of the Drude dielectric function leads to zero Casimir entropy at zero temperature in accordance with Nernst's theorem. We demonstrate that their proof is not applicable to metals with perfect crystal lattices having no impurities. Thus there is no contradiction with previous results in the lite...

We consider the brane universe in the bulk background of the topological AdSSchwarzschild black holes, where the brane tension takes larger value than the finetunned value. The resulting universe is radiation dominated and has positive cosmological constant. We obtain the associated cosmological Cardy formula and the CardyVerlinde formula. We also derive the Hubble and the Bekenstein entropy bo...

The new approach to the theoretical description of the thermal Casimir force between real metals is presented. It uses the plasma-like dielectric permittivity that takes into account the interband transitions of core electrons. This permittivity precisely satisfies the Kramers-Kronig relations. The respective Casimir entropy is positive and vanishes at zero temperature in accordance with the Ne...

In view of the current discussion on the subject, an effort is made to show very accurately both analytically and numerically how the Drude dispersion model, assuming the relaxation is nonzero at zero temperature (which is the case when impurities are present), gives consistent results for the Casimir free energy at low temperatures. Specifically, we find that the free energy consists essential...

The Cardy-Verlinde formula, which expresses the entropy of the conformal field theory in terms of its total energy (or the extensive energy), Casimir energy and radius of the unit sphere S, is further verified by using the Kerr-Newman-AdS4 and the two rotation parameters Kerr-AdS5 black holes. For the Kerr-Newman-AdS4 black hole we find that to cast the entropy of the conformal field theory int...

The Cardy-Verlinde formula is generalized to the asymptotically flat rotating charged black holes in the Einstein-Maxwell theory and low-energy effective field theory describing string by using some typical spacetimes, such as the Kerr-Newman, Einstein-Maxwell-dilaton-axion, Kaluza-Klein, and Sen black holes. For the Kerr-Newman black hole, the definition of the Casimir energy takes the same fo...

A complete thermodynamic treatment of the Casimir effect is presented. Explicit expressions for the free and the internal energy, the entropy and the pressure are discussed. As an example we consider the Casimir effect with different temperatures between the plates (T) resp. outside of them (T ′). For T ′ < T the pressure of heat radiation can eventually compensate the Casimir force and the tot...

The Cardy-Verlinde formula, which expresses the entropy of the conformal field theory in terms of its total energy (or the extensive energy), Casimir energy and radius of the unit sphere S, is further verified by using the KerrNewman-AdS4 and Kerr-Newman-dS4 black holes. For the Kerr-NewmanAdS4 black hole, we find that to cast the entropy of the conformal field theory into the Cardy-Verlinde fo...