Casimir Energy and Entropy in the Sphere--Sphere Geometry

TL;DR

This paper investigates the Casimir energy and entropy between two spheres under different models, revealing nonmonotonic behaviors and negative entropy regions, with implications for thermodynamics.

Contribution

It provides the first detailed analysis of Casimir energy and entropy in sphere-sphere geometry across multiple models, highlighting novel nonmonotonic behaviors.

Findings

Nonmonotonic Helmholtz free energy with separation and temperature.

Negative entropy regions for perfect metal and plasma models.

Absence of nonmonotonic entropy behavior in Drude model.

Abstract

We calculate the Casimir energy and entropy for two spheres described by the perfect metal model, plasma model, and Drude model in the large separation limit. We obtain nonmonotonic behavior of the Helmholtz free energy with separation and temperature for the perfect metal and plasma models, leading to parameter ranges with negative entropy, and also nonmonotonic behavior of the entropy with temperature and the separation between the spheres. This nonmonotonic behavior has not been found for Drude model. The appearance of this anomalous behavior of the entropy is discussed as well as its thermodynamic consequences.