Casimir self-entropy of a spherical electromagnetic δ-function shell

In this paper we continue our program of computing Casimir self-entropies of idealized electrical bodies. Here we consider an electromagnetic delta-function sphere ("semitransparent sphere") whose electric susceptibility has a transverse polarization with arbitrary strength. Dispersion is incorporated by a plasma-like model. In the strong-coupling limit, a perfectly conducting spherical shell is realized. We compute the entropy for both low and high temperatures. The transverse electric self-entropy is negative as expected, but the transverse magnetic self-entropy requires ultraviolet and infrared renormalization (subtraction), and, surprisingly, is only positive for sufficiently strong coupling. Results are robust under different regularization schemes. These rather surprising findings require further investigation.