# Fisher information and Rényi dimensions: A thermodynamical formalism

## Abstract

The relation between the Fisher information and Rényi dimensions is established: the Fisher information can be expressed as a linear combination of the first and second derivatives of the Rényi dimensions with respect to the Rényi parameter β. The Rényi parameter β is the parameter of the Fisher information. A thermodynamical description based on the Fisher information with β being the inverse temperature is introduced for chaotic systems. The link between the Fisher information and the heat capacity is emphasized, and the Fisher heat capacity is introduced.

- Authors:

- Department of Theoretical Physics, University of Debrecen, H–4002 Debrecen (Hungary)

- Publication Date:

- OSTI Identifier:
- 22596558

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; CHAOS THEORY; FRACTALS; INFORMATION; SPECIFIC HEAT

### Citation Formats

```
Godó, B., and Nagy, Á.
```*Fisher information and Rényi dimensions: A thermodynamical formalism*. United States: N. p., 2016.
Web. doi:10.1063/1.4959908.

```
Godó, B., & Nagy, Á.
```*Fisher information and Rényi dimensions: A thermodynamical formalism*. United States. doi:10.1063/1.4959908.

```
Godó, B., and Nagy, Á. Mon .
"Fisher information and Rényi dimensions: A thermodynamical formalism". United States.
doi:10.1063/1.4959908.
```

```
@article{osti_22596558,
```

title = {Fisher information and Rényi dimensions: A thermodynamical formalism},

author = {Godó, B. and Nagy, Á.},

abstractNote = {The relation between the Fisher information and Rényi dimensions is established: the Fisher information can be expressed as a linear combination of the first and second derivatives of the Rényi dimensions with respect to the Rényi parameter β. The Rényi parameter β is the parameter of the Fisher information. A thermodynamical description based on the Fisher information with β being the inverse temperature is introduced for chaotic systems. The link between the Fisher information and the heat capacity is emphasized, and the Fisher heat capacity is introduced.},

doi = {10.1063/1.4959908},

journal = {Chaos (Woodbury, N. Y.)},

number = 8,

volume = 26,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}

DOI: 10.1063/1.4959908

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