  Assuming the conventional Casimir setting with two thick parallel perfectly
conducting plates of large extent with a homogeneous and isotropic medium
between them, we discuss the physical meaning of the electromagnetic field
energy $W_{\rm disp}$ when the intervening medium is weakly dispersive but
nondissipative. The presence of dispersion means that the energy density
contains terms of the form $d[\omega\epsilon(\omega)] /d\omega$ and
$d[\omega\mu(\omega)] /d\omega$. We find that, as $W_{\rm disp}$ refers
thermodynamically to a non-closed physical system, it is {\it not} to be
identified with the internal thermodynamic energy $U$ following from the free
energy $F$, or the electromagnetic energy $W$, when the last-mentioned
quantities are calculated without such dispersive derivatives. To arrive at
this conclusion, we adopt a model in which the system is a capacitor, linked to
an external self-inductance $L$ such that stationary oscillations become
possible. Therewith the model system becomes a non-closed one. As an
introductory step, we review the meaning of the nondispersive energies, $F, U,$
and $W$. As a final topic, we consider an anomaly connected with local surface
divergences encountered in Casimir energy calculations for higher spacetime
dimensions, $D>4$, and discuss briefly its dispersive generalization. This kind
of application is essentially a generalization of the treatment of Alnes {\it
et al.} [J. Phys. A: Math. Theor. {\bf 40}, F315 (2007)] to the case of a
medium-filled cavity between two hyperplanes.
