On the entropy of a spherical plasma shell

TL;DR

This paper investigates the entropy of a spherical plasma shell model, demonstrating that it can be negative at low temperatures and plasma frequencies, which has implications for understanding entropy in Casimir-like systems.

Contribution

It provides a regularization-free numerical calculation of the entropy of a spherical plasma shell, confirming the existence of negative entropy regions in such configurations.

Findings

Entropy is free of ultraviolet divergences.

Negative entropy occurs at low temperature and plasma frequency.

The model serves as a simplified representation for giant carbon molecules.

Abstract

Negative entropy was repeatedly observed in the Casimir effect caused by dissipation or geometry. However, it was restricted to subsystems. Recently the question about the entropy for a complete Casimir effect like configuration was raised. In the present paper we consider a spherical plasma shell which can be considered as a (crude) model for a giant carbon molecule (e.g., $C_{60}$). The entropy is free of ultraviolet divergences and its calculation does not need any regularization. We calculate the entropy numerically and demonstrate unambiguously the existence of a region where it takes negative values. This region is at small values of temperature and plasma frequency (in units of the radius).