  Positive semi-definite expressions for the time-domain macroscopic energy
density in passive, spatially nondispersive, dipolar continua are derived from
the underlying microscopic Maxwell equations satisfied by classical models of
discrete bound dipolar molecules or inclusions of the material or metamaterial
continua. The microscopic derivation reveals two distinct positive
semi-definite macroscopic energy expressions, one that applies to diamagnetic
continua and another that applies to paramagnetic continua. The diamagnetic
dipoles are "unconditionally passive" in that their Amperian magnetic dipole
moments are zero in the absence of applied fields. The analysis of paramagnetic
continua, whose magnetization is caused by the alignment of randomly oriented
"permanent" Amperian magnetic dipole moments that dominate any induced
diamagnetic magnetization, is greatly simplified by first proving that the
microscopic power equations for rotating "permanent" Amperian magnetic dipoles
(which are shown to not satisfy unconditional passivity) reduce effectively to
the same power equations obeyed by rotating unconditionally passive
magnetic-charge magnetic dipoles. The difference between the macroscopic
paramagnetic and diamagnetic energy expressions is equal to a "hidden energy"
that parallels the hidden momentum often attributed to Amperian magnetic
dipoles. The microscopic derivation reveals that this hidden energy is drawn
from the reservoir of inductive energy in the initial paramagnetic microscopic
Amperian magnetic dipole moments. The macroscopic, positive semi-definite,
time-domain energy expressions are applied to lossless bianisotropic media to
determine the inequalities obeyed by the frequency-domain bianisotropic
constitutive parameters. Subtleties associated with the causality as well as
the group and energy-transport velocities for diamagnetic media are discussed.
