Gibbs-Shannon Entropy and Related Measures: Tsallis Entropy
Garimella Rama Murthy
TL;DR
This paper explores the relationship between Gibbs-Shannon entropy and Tsallis entropy, demonstrating that an approximation to the former naturally yields the latter for q=2, and discusses related measures in information theory.
Contribution
It establishes a theoretical link between Gibbs-Shannon and Tsallis entropy, providing new measures and properties relevant to information theory research.
Findings
Approximation to Gibbs-Shannon entropy leads to Tsallis entropy at q=2
Introduces new measures based on channel input/output
Discusses properties of these measures
Abstract
In this research paper, it is proved that an approximation to Gibbs-Shannon entropy measure naturally leads to Tsallis entropy for the real parameter q =2 . Several interesting measures based on the input as well as output of a discrete memoryless channel are provided and some of the properties of those measures are discussed. It is expected that these results will be of utility in Information Theoretic research.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Neural Networks and Applications · Complex Systems and Time Series Analysis