  A Lagrangean for the dynamics of an electromagnetic field in a dispersive and
dissipative material is constructed (adapting some ideas by Bekenstein and
Hannay) and an expression for the energy density that is positive is obtained
from it. The expression contains extra (sink) degrees of freedom that represent
dissipating modes. In simplified cases the sink modes can be eliminated to
yield an energy density expression in terms of the electromagnetic fields, the
polarization and the magnetization only, but which contains parameters
associated with the sink modes. The method of adding extra modes can be used to
set up a Lagrangean formalism for dissipative systems in general, such that
will reinstate time-translation invariance and will yield a unique energy
density.
