  We prove that well-known speed of light restrictions on electromagnetic
energy velocity can be extended to a new level of generality, encompassing even
nonlocal chiral media in periodic geometries, while at the same time weakening
the underlying assumptions to only passivity and linearity of the medium
(either with a transparency window or with dissipation). As was also shown by
other authors under more limiting assumptions, passivity alone is sufficient to
guarantee causality and positivity of the energy density (with no thermodynamic
assumptions). Our proof is general enough to include a very broad range of
material properties, including anisotropy, bianisotropy (chirality),
nonlocality, dispersion, periodicity, and even delta functions or similar
generalized functions. We also show that the "dynamical energy density" used by
some previous authors in dissipative media reduces to the standard Brillouin
formula for dispersive energy density in a transparency window. The results in
this paper are proved by exploiting deep results from linear-response theory,
harmonic analysis, and functional analysis that had previously not been brought
together in the context of electrodynamics.
