  Recently the Casimir self-entropy of an electromagnetic $\delta$-function
shell was considered by two different groups, with apparently discordant
conclusions, although both had concluded that a region of negative entropy
existed for sufficiently weak coupling. We had found that the entropy contained
an infrared divergence, which we argued should be discarded on physical
grounds. On the contrary, Bordag and Kirsten recently found a completely finite
self-entropy, although they, in fact, have to remove an infrared divergence.
Apart from this, the high- and low-temperature results for finite coupling
agree precisely for the transverse electric mode, but there are significant
discrepancies in the transverse magnetic mode. We resolve those discrepancies
here. In particular, it is shown that coupling-independent terms do not occur
in a consistent regulated calculation, they likely being an artefact of the
omission of pole terms. The results of our previous analysis, especially, the
existence of a negative entropy region for sufficiently weak coupling, are
therefore confirmed. Finally, we offer some analogous remarks concerning the
Casimir entropy of a thin electromagnetic sheet, where the total entropy is
always positive. In that case, the origin of the analogous discrepancy can be
explicitly isolated.
