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Graphic representation of the evolutionary processes of the compositions of multicomponent objects of any nature

Abstract

A method for the graphic representation of evolutionary processes of compositions is described. Preparation of materials includes descending ranking of contents of components and standardization of the length of the obtained sequences while discarding excess contents. The following three parameters are calculated for the persistent distribution of contents: (1) information entropy H = −Σp ilogp i as a measure of complexity of the system’s composition, (2) anentropy A = −Σlogp i as a measure of the composition purity, and (3) tolerance T = log[(Σ1/p i)/n] as a measure of special purity. In order to represent the process of compositional change, paired diagrams with the axes En, An, and T are used. The obtained entropy diagrams describe separation and mixing processes that occur in nature, technology, and society in the most adequate manner.

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Correspondence to T. G. Petrov.

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Original Russian Text © T.G. Petrov, 2012, published in Nauchno-Tekhnicheskaya Informatsiya, Seriya 2, 2012, No. 3, pp. 21–31.

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Petrov, T.G. Graphic representation of the evolutionary processes of the compositions of multicomponent objects of any nature. Autom. Doc. Math. Linguist. 46, 79–93 (2012). https://doi.org/10.3103/S0005105512020045

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  • DOI: https://doi.org/10.3103/S0005105512020045

Keywords

  • evolution of compositions
  • information entropy
  • complexity of composition
  • entropy of mixing
  • anentropy
  • entropy of separation
  • purity of composition
  • entropy diagram
  • tolerance
  • Shurubor theorem
  • rock
  • ethnic composition
  • Gini coefficient