  We provide a self-consistent extension of the Lorentz reciprocity theorem and
the Poynting theorem for media possessing electric and magnetic dipolar and
quadrupolar responses related to electric and magnetic fields and field
gradients. Using these two theorems, we respectively deduce the conditions of
reciprocity and gainlessness and losslessness that apply to the various tensors
mediating the interactions of these multipole moments and the associated fields
and field gradients. We expect that these conditions will play an essential
role in developing advanced metamaterial modeling techniques that include
quadrupolar and spatially dispersive responses.
