Variational Principles for Dissipative (sub) Systems with
Applications to the Theory of Dispersion and Geometrical Optics
Authors: I.Y. Dodin, D. E. Ruiz
Abstract: 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 arti cial doubling of variables. Here, a
di erent 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
Submitted to: Physical Letters A
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