  The question which degrees of freedom are responsible for the classical part
of the Gibbons-Hawking entropy is addressed. A physical toy model sharing the
same properties from the viewpoint of the linearized theory is a charged vacuum
capacitor. In Maxwell's theory, the gauge sector including ghosts is a
topological field theory. When computing the grand canonical partition function
with a chemical potential for electric charge in the indefinite metric Hilbert
space of the BRST quantized theory, the classical contribution originates from
the part of the gauge sector that is no longer trivial due to the boundary
conditions required by the physical set-up. More concretely, in the benchmark
problem of a planar charged vacuum capacitor, we identify the degrees of
freedom that, in the quantum theory, give rise to an additional contribution to
the standard black body result proportional to the area of the plates, and that
allow for a microscopic derivation of the thermodynamics of the charged
capacitor.
