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Fisher information and Rényi dimensions: A thermodynamical formalism
1Department of Theoretical Physics, University of Debrecen, H-4002 Debrecen, Hungary.
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.
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