  Applications of variational methods are typically restricted to conservative
systems. Some extensions to dissipative systems have been reported too but
require ad hoc techniques such as the artificial doubling of the dynamical
variables. Here, a different approach is proposed. We show that, for a broad
class of dissipative systems of practical interest, variational principles can
be formulated using constant Lagrange multipliers and Lagrangians nonlocal in
time, which allow treating reversible and irreversible dynamics on the same
footing. A general variational theory of linear dispersion is formulated as an
example. In particular, we present a variational formulation for linear
geometrical optics in a general dissipative medium, which is allowed to be
nonstationary, inhomogeneous, nonisotropic, and exhibit both temporal and
spatial dispersion simultaneously.
