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Fisher information and Rényi entropies in dynamical systems
1Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, Hungary.
Chaos (Woodbury, N.Y.)
|August 3, 2017
Summary
This study links Fisher information to Rényi entropies using a thermodynamical approach. A new Fisher heat capacity measure shows enhanced sensitivity to system changes compared to conventional methods.
Area of Science:
- Information theory
- Statistical mechanics
- Thermodynamics
Background:
- Fisher information quantifies statistical data variability.
- Rényi entropies generalize Shannon entropy.
- Thermodynamical formalisms offer insights into information measures.
Purpose of the Study:
- To explore the connection between Fisher information and Rényi entropies.
- To establish a thermodynamical framework utilizing Fisher information.
- To define and analyze a novel Fisher heat capacity.
Main Methods:
- Developing a thermodynamical formalism based on Fisher information.
- Introducing a parameter β as inverse temperature.
- Defining and calculating the Fisher heat capacity.
Main Results:
- A direct link between Fisher information and Rényi entropies was established.
- The Fisher heat capacity was defined and characterized.
- The Fisher heat capacity demonstrated higher-order sensitivity to changes than conventional heat capacity.
Conclusions:
- The thermodynamical formalism provides a new perspective on information theory.
- Fisher information and Rényi entropies are interconnected within this framework.
- The Fisher heat capacity is a more sensitive indicator of system dynamics.
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