Comment on "Does the transverse electric zero mode contribute to the Casimir effect for a metal?"

Recently J.S. Hoye, I.Brevik, J.B. Aarseth, and K.A. Milton [Phys. Rev. E v.67, 056116 (2003); quant-ph/0212125] proposed that if the Lifshitz formula is combined with the Drude model, the transverse electric zero mode does not contribute to the result for real metals and there arises a linear temperature correction to the Casimir force at small temperatures. The authors claim that in spite of the fact that the Casimir entropy in their approach is negative, the Nernst heat theorem is satisfied. In the present Comment we show that the authors' conclusion regarding the Nernst heat theorem is in error. We demonstrate also the resolution of this thermodynamic puzzle based on the use of the surface impedance instead of the Drude dielectric function. The results of numerical computations obtained by the authors are compared with those from use of the surface impedance approach which are thermodynamically consistent.