Analytical and numerical verification of the Nernst theorem for metals

Abstract

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 gives consistent results for the Casimir free energy at low temperatures. Specifically, for the free energy near T=0 we find the leading term proportional to T2 and the next-to-leading term proportional to T(5/2). These terms give rise to zero Casimir entropy as T-->0 and are thus in accordance with Nernst's theorem.