Concepts and Recent Advances in Generalized Information Measures and Statistics

Author(s): Raul D. Rossignoli, Andres M. Kowalski and Evaldo M. F. Curado

DOI: 10.2174/9781608057603113010007

Essentials of Information Entropy and Related Measures

Pp: 30-56 (27)

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Abstract

SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.

Abstract

This introductory chapter provides a basic review of the Shannon entropy and of some important related quantities like the joint entropy, the conditional entropy, the mutual information and the relative entropy. We also discuss the Fisher information, the fundamental property of concavity, the basic elements of the maximum entropy approach and the definition of entropy in the Quantum case. We close this chapter with the axioms which determine the Shannon entropy and a brief description of other information measures.

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