Casmir-Lifshitz Forces and Entropy

TL;DR

This paper clarifies misconceptions about the Casimir-Lifshitz entropy, showing its potential negativity under certain conditions and analyzing its behavior at low temperatures for metallic surfaces and liquid films.

Contribution

It provides a corrected interpretation of Casimir entropy, derives its low-temperature behavior for metallic surfaces with anomalous skin effect, and compares entropy behavior in liquid films and half-spaces.

Findings

Casimir entropy can be negative under specific conditions.

Low-temperature surface entropy of metals exhibits singular behavior.

Entropy of finite liquid films differs from that of half-spaces as temperature approaches zero.

Abstract

It is shown that the violation of the positiveness of the entropy due to the Casimir-Lifshitz interaction claimed in several papers is an artifact related to an improper interpretation of the "Casimir entropy", which actually is a difference of two positive terms. It is explained that at definite condition this "Casimir entropy" must be negative. A direct derivation of the low temperature behavior of the surface entropy of a metallic surface in conditions of the anomalous skin effect is given and singular temperature dependency of this quantity is discussed. In conclusion a hydrodynamic example of the entropy of a liquid film is considered. It occurs that the entropy of a film of finite thickness and a liquid half-space behave differently at T tends to 0.