# An Isomorphism between Lyapunov Exponents and Shannon's Channel Capacity

## Abstract

We demonstrate that discrete Lyapunov exponents are isomorphic to numeric overflows of the capacity of an arbitrary noiseless and memoryless channel in a Shannon communication model with feedback. The isomorphism allows the understanding of Lyapunov exponents in terms of Information Theory, rather than the traditional definitions in chaos theory. The result also implies alternative approaches to the calculation of related quantities, such as the Kolmogorov Sinai entropy which has been linked to thermodynamic entropy. This work provides a bridge between fundamental physics and information theory. It suggests, among other things, that machine learning and other information theory methods can be employed at the core of physics simulations.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1377767

- Report Number(s):
- LLNL-TR-733786

- DOE Contract Number:
- AC52-07NA27344

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE

### Citation Formats

```
Friedland, Gerald, and Metere, Alfredo.
```*An Isomorphism between Lyapunov Exponents and Shannon's Channel Capacity*. United States: N. p., 2017.
Web. doi:10.2172/1377767.

```
Friedland, Gerald, & Metere, Alfredo.
```*An Isomorphism between Lyapunov Exponents and Shannon's Channel Capacity*. United States. doi:10.2172/1377767.

```
Friedland, Gerald, and Metere, Alfredo. Wed .
"An Isomorphism between Lyapunov Exponents and Shannon's Channel Capacity". United States.
doi:10.2172/1377767. https://www.osti.gov/servlets/purl/1377767.
```

```
@article{osti_1377767,
```

title = {An Isomorphism between Lyapunov Exponents and Shannon's Channel Capacity},

author = {Friedland, Gerald and Metere, Alfredo},

abstractNote = {We demonstrate that discrete Lyapunov exponents are isomorphic to numeric overflows of the capacity of an arbitrary noiseless and memoryless channel in a Shannon communication model with feedback. The isomorphism allows the understanding of Lyapunov exponents in terms of Information Theory, rather than the traditional definitions in chaos theory. The result also implies alternative approaches to the calculation of related quantities, such as the Kolmogorov Sinai entropy which has been linked to thermodynamic entropy. This work provides a bridge between fundamental physics and information theory. It suggests, among other things, that machine learning and other information theory methods can be employed at the core of physics simulations.},

doi = {10.2172/1377767},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Jun 07 00:00:00 EDT 2017},

month = {Wed Jun 07 00:00:00 EDT 2017}

}