# Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics

## 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 the artificial doubling of the dynamical variables. We propose a different approach. Here, 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. Particularly, we present a variational formulation for linear geometrical optics in a general dissipative medium, which is allowed to be nonstationary, inhomogeneous, anisotropic, and exhibit both temporal and spatial dispersion simultaneously.

- Authors:

- Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Univ. of California, Berkeley, CA (United States). Dept. of Physics
- Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1347109

- Alternate Identifier(s):
- OSTI ID: 1454275

- Grant/Contract Number:
- AC02-09CH11466; NA0002948

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics Letters. A

- Additional Journal Information:
- Journal Volume: 381; Journal Issue: 16; Journal ID: ISSN 0375-9601

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Variational principles; Dissipation; Linear dispersion; Geometrical optics

### Citation Formats

```
Dodin, I. Y., Zhmoginov, A. I., and Ruiz, D. E..
```*Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics*. United States: N. p., 2017.
Web. doi:10.1016/j.physleta.2017.02.023.

```
Dodin, I. Y., Zhmoginov, A. I., & Ruiz, D. E..
```*Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics*. United States. doi:10.1016/j.physleta.2017.02.023.

```
Dodin, I. Y., Zhmoginov, A. I., and Ruiz, D. E.. Fri .
"Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics". United States.
doi:10.1016/j.physleta.2017.02.023. https://www.osti.gov/servlets/purl/1347109.
```

```
@article{osti_1347109,
```

title = {Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics},

author = {Dodin, I. Y. and Zhmoginov, A. I. and Ruiz, D. E.},

abstractNote = {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. We propose a different approach. Here, 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. Particularly, we present a variational formulation for linear geometrical optics in a general dissipative medium, which is allowed to be nonstationary, inhomogeneous, anisotropic, and exhibit both temporal and spatial dispersion simultaneously.},

doi = {10.1016/j.physleta.2017.02.023},

journal = {Physics Letters. A},

number = 16,

volume = 381,

place = {United States},

year = {Fri Feb 24 00:00:00 EST 2017},

month = {Fri Feb 24 00:00:00 EST 2017}

}

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