On the Casimir entropy for a ball in front of a plane

TL;DR

This paper investigates the violation of the third law of thermodynamics in Casimir effect scenarios, specifically for a ball in front of a plane, and finds that the violation is not due to the infinite size of the surfaces.

Contribution

It extends previous calculations of Casimir entropy violations from plane surfaces to a spherical object near a plane, clarifying the geometric dependence.

Findings

Violation of the third law persists in the ball-plane geometry.

The violation is independent of the infinite extent of the surfaces.

Calculations show similar entropy behavior as in parallel plane configurations.

Abstract

The violation of the third law of thermodynamics for metals described by the Drude model and for dielectrics with finite \DC conductivity is one of the most interesting problems in the field of the Casimir effect. It manifests itself as a non-vanishing of the entropy for vanishing temperature. We review the relevant calculations for plane surfaces and calculate the corresponding contributions for a ball in front of a plane. In this geometry, these appear in much the same way as for parallel planes. We conclude that the violation of the 3rd law is not related to the infinite size of the planes.