Negativity of the Casimir self-entropy in spherical geometries

TL;DR

This paper investigates the unexpected negativity of self-entropy in spherical Casimir geometries, revealing that negative self-entropy can occur under certain conditions and challenging previous assumptions about entropy cancellation.

Contribution

The study provides a detailed analysis of negative self-entropy in spherical geometries using advanced mathematical techniques and numerical results, highlighting phenomena not previously understood.

Findings

Negative self-entropy can occur in weaker coupling regimes.

Positive self-entropy of spheres does not always cancel negative interaction entropy.

Numerical results confirm the persistence of negative self-entropy across various conditions.

Abstract

It has been recognized for some time that even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self-entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel-Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features.