Analytical and Numerical Demonstration of How the Drude Dispersive Model Satisfies Nernst's Theorem for the Casimir Entropy

TL;DR

This paper analytically and numerically demonstrates that the Drude dispersive model, with nonzero relaxation at zero temperature, satisfies Nernst's theorem by ensuring the Casimir entropy approaches zero as temperature approaches absolute zero.

Contribution

It provides a detailed analytical and numerical analysis showing the Drude model's consistency with thermodynamic principles for Casimir free energy at low temperatures.

Findings

Casimir free energy has leading term proportional to T^2

Next term proportional to T^{5/2}

Casimir entropy approaches zero as T -> 0

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 dispersive 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 essentially of two terms, one leading term proportional to T^2, and a next term proportional to T^{5/2}. Both these terms give rise to zero Casimir entropy as T -> 0, thus in accordance with Nernst's theorem.