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On Conditional Tsallis Entropy.

Andreia Teixeira1,2,3, André Souto4,5,6, Luís Antunes7

  • 1CINTESIS-Centre for Health Technology and Services Research, Faculty of Medicine, University of Porto, 4200-450 Porto, Portugal.

Entropy (Basel, Switzerland)
|November 27, 2021
PubMed
Summary
This summary is machine-generated.

This study explores various definitions for conditional Tsallis entropy, a concept lacking a standard definition. It compares their properties and introduces an online tool for calculating these entropies.

Keywords:
Generalizations of Shannon entropyTsallis entropyconditional Tsallis entropies

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Area of Science:

  • Information Theory
  • Statistical Mechanics
  • Non-extensive Thermodynamics

Background:

  • The standard Tsallis entropy, a generalization of Shannon entropy, depends on a parameter α.
  • A universally accepted definition for conditional Tsallis entropy is currently lacking in the literature.
  • Understanding conditional entropy is crucial for analyzing complex systems and information measures.

Purpose of the Study:

  • To investigate and compare existing proposed definitions of conditional Tsallis entropy.
  • To introduce and analyze a novel, natural proposal for conditional Tsallis entropy.
  • To provide a practical computational tool for researchers working with Tsallis entropy.

Main Methods:

  • Literature review and analysis of three previously proposed conditional Tsallis entropy definitions.
  • Development and theoretical comparison of an additional, distinct conditional Tsallis entropy proposal.
  • Implementation of an online tool for calculating conditional Tsallis entropies based on probability distributions and the parameter α.

Main Results:

  • The study details the properties of four distinct conditional Tsallis entropy definitions.
  • Comparative analysis reveals differences in how these definitions behave as a function of the parameter α.
  • An accessible online tool is provided for computing these entropies.

Conclusions:

  • The paper offers a comprehensive comparison of current conditional Tsallis entropy definitions.
  • The proposed novel definition provides an alternative for analyzing conditional information measures.
  • The developed online tool facilitates the practical application and further research in Tsallis entropy.