# Second-law irreversibility and phase-space dimensionality loss from time-reversible nonequilibrium steady-state Lyapunov spectra

## Abstract

We consider steady-state nonequilibrium many-body flows of mass and momentum. For several such diffusive and viscous flows we estimate the phase-space strange-attractor Lyapunov dimensions from the complete spectrum of Lyapunov exponents. We vary the number of particles and the number of thermostated degrees of freedom, as well as the deviation from equilibrium. The resulting Lyapunov spectra provide numerical evidence that the fractal dimensionality loss in such systems remains extensive in a properly defined nonequilibrium analog of the equilibrium large-system thermodynamic limit. The data also suggest a variational principle in the vicinity of nonequilibrium steady states.

- Authors:

- (University of California at Davis Livermore and Lawrence Livermore National Laboratory, Livermore, California 94551-7808 (United States))Posch, H.A. (Institute for Experimental Physics, University of Vienna, Vienna A-1090 (Austria))

- Publication Date:

- OSTI Identifier:
- 5238945

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

- Additional Journal Information:
- Journal Volume: 49:3; Journal ID: ISSN 1063-651X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FLUID FLOW; IRREVERSIBLE PROCESSES; DEGREES OF FREEDOM; DIFFUSION; LYAPUNOV METHOD; PHASE SPACE; STEADY-STATE CONDITIONS; THERMODYNAMICS; VISCOUS FLOW; CALCULATION METHODS; MATHEMATICAL SPACE; SPACE; 661300* - Other Aspects of Physical Science- (1992-)

### Citation Formats

```
Hoover, W.G.
```*Second-law irreversibility and phase-space dimensionality loss from time-reversible nonequilibrium steady-state Lyapunov spectra*. United States: N. p., 1994.
Web. doi:10.1103/PhysRevE.49.1913.

```
Hoover, W.G.
```*Second-law irreversibility and phase-space dimensionality loss from time-reversible nonequilibrium steady-state Lyapunov spectra*. United States. https://doi.org/10.1103/PhysRevE.49.1913

```
Hoover, W.G. Tue .
"Second-law irreversibility and phase-space dimensionality loss from time-reversible nonequilibrium steady-state Lyapunov spectra". United States. https://doi.org/10.1103/PhysRevE.49.1913.
```

```
@article{osti_5238945,
```

title = {Second-law irreversibility and phase-space dimensionality loss from time-reversible nonequilibrium steady-state Lyapunov spectra},

author = {Hoover, W.G.},

abstractNote = {We consider steady-state nonequilibrium many-body flows of mass and momentum. For several such diffusive and viscous flows we estimate the phase-space strange-attractor Lyapunov dimensions from the complete spectrum of Lyapunov exponents. We vary the number of particles and the number of thermostated degrees of freedom, as well as the deviation from equilibrium. The resulting Lyapunov spectra provide numerical evidence that the fractal dimensionality loss in such systems remains extensive in a properly defined nonequilibrium analog of the equilibrium large-system thermodynamic limit. The data also suggest a variational principle in the vicinity of nonequilibrium steady states.},

doi = {10.1103/PhysRevE.49.1913},

url = {https://www.osti.gov/biblio/5238945},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)},

issn = {1063-651X},

number = ,

volume = 49:3,

place = {United States},

year = {1994},

month = {3}

}

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