Symmetry Studies and Dcompositions of Entropy

This paper describes a group-theoretic method for decomposing the entropy of a finite ensemble when symmetry considerations are of interest. The cases in which the elements in the ensemble are indexed by {1,2,...,n} and by the permutations of a finite set are considered in detail and interpreted as...

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Bibliographic Details
Published inEntropy (Basel, Switzerland) Vol. 8; no. 2; pp. 88 - 109
Main Author Marlos Viana
Format Journal Article
LanguageEnglish
Published MDPI AG 01.06.2006
Subjects
canonical decomposition
characters
group representation
invariance
Kullback's divergence
Sloan fonts
visual acuity
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Summary:This paper describes a group-theoretic method for decomposing the entropy of a finite ensemble when symmetry considerations are of interest. The cases in which the elements in the ensemble are indexed by {1,2,...,n} and by the permutations of a finite set are considered in detail and interpreted as particular cases of ensembles with elements indexed by a set subject to the actions of a finite group. Decompositions for the entropy in binary ensembles and in ensembles indexed by short DNA words are discussed. Graphical descriptions of the decompositions of the entropy in geological samples are illustrated. The decompositions derived in the present cases follow from a systematic data analytic tool to study entropy data in the presence of symmetry considerations.
ISSN:1099-4300
1099-4300
DOI:10.3390/e8020088