On the entropy of a spherical plasma shell

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 inverse radius).

Remarks on the Casimir self-entropy of a spherical electromagnetic δ -function shell

“…It also coincides with the plasma-shell model considered by Bordag and Kirsten in Ref. [4]. To translate parameters in the model in that reference to ours, we note that their R is the same as our a, and ΩR coincides with λ 0 .…”

“…We see no sign of the coupling-independent high-temperature TM term in the free energy found in Ref. [4]; this arises because the heatkernel approach incorrectly incorporates λ 0 terms, apparently due to the omission of a pole term in the frequency integration. However, the high-temperature term linear in the coupling coincides with our findings, and results from the exact treatment of the O(λ 0 ) terms.…”

“…In this note we will make a detailed comparison between the results found in Refs. [4] and [3]. We will see that the finite coupling results found at low and high temperature agree for the TE mode, which is by far easier to treat.…”

“…The entropy due to electromagnetic field fluctuations, or Casimir entropy, of a perfectly conducting spherical shell (of radius a) was computed many years ago by Balian and Duplantier [1], who found the following low and high temperature behaviors for the free energy, Here the subscript is a reminder that the conductivity of the sphere is considered infinite, and the ∆ means this is the correction to the zero-temperature Casimir energy of the sphere, first calculated by Boyer [2]. Only recently was this calculation generalized to a spherical shell with a finite electromagnetic coupling, a so-called electromagnetic δ-function shell, or a spherical plasma shell [3,4]. The former is described by the background permittivity ε(r) − 1 = λ(1 − rr)δ(r − a), (1.2) which describes a sphere of radius a centered at the origin.…”

Free energy and entropy for finite temperature quantum field theory under the influence of periodic backgrounds

“…Meanwhile, the entropy of Casimir effect related configurations was calculated for quite a large number of model systems. For three dimensional ones, a plasma plane or a plasma sphere, in [19,20] and [21,22] and for some simple one dimensional examples in [23]. In all these cases the single standing objects were considered and the complete entropy, except the black body * bordag@uni-leipzig.de † jose.munoz.castaneda@uva.es ‡ lucia.santamaria@uva.es part (contributions from the empty space), was computed.…”