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.
Similar content being viewed by others
References
Petrov, T.G., Reason of General Classification Variant of Geochemical Systems, Vestnik Leningr. Gos. Univ., Ser. 7. Geolog. Geogr. 1971, vol. 18, no. 3, pp. 30–38.
Petrov, T.G., Information Language for Description of Multicomponent Object Compositions, Nauchn. Tekhn. Inform., Ser. 2, 2001, no. 3, pp. 8–18.
Hartley, R.V.L., Transmission of Information, Bell System Techn. J., 1928, vol. 7, no. 3, pp. 535–563.
Petrov, T.G., Range-Entropy Approach to the Description of the Geological Object Compositions and Their Alterations (on the Geological Coenology), Obshch. Prikladn. Tsoenolog., 2007, no. 5, pp. 27–33.
Spenser, H., Principles of Biology in two volumes. Vol. I. Part I: The Data of Biology; Part II: The Inductions of Biology; Part III: The Evolution of Life; Appendices. 1864; Vol. II. Part IV: Morphological Development; Part V: Physiological Development; Part VI: Laws of Multiplication; Appendices. 1867.
Collins, F.H., Epitome of the Synthetic Philosophy of Herbert Spencer, Williams and Norgate, 1901
Petrov, T.G., RHA Method as Systematization Problem Solution for Analytical Data about Substantial Composition of Geological Objects, Otech. Geologiya, 2008, no. 4, pp. 98–105.
Petrov, T.G., Hierarchical Periodic System of Chemical Compositions and Its Connection with Periodical System of Elements, Vestn. St. Petersb. Gos. Univ., Ser. 7, 2009, no. 2, pp. 21–28.
Velikoslavinskii, D.A., Eliseev, E.N., and Kratts, K.O., Variatsionnyi analiz magmaticheskikh sistem (Variation Analysis of Magmatic Systems), Leningrad: Nauka, 1984.
Petrov, T.G. and Farafonova, O.I., Informatsionnokomponentnyi analiz. Metod RHA (Information-Component Analysis. RHA Method), St. Petersburg: St. Petersb. Gos. Univ., 2005.
Petrov, T.G., Farafonova, O.I., and Sokolov, P.B., Information-Entropy Characteristics in Composition of Minerals and Rocks as a Reflection of Their Crystallization Process, Proc. All-Russ. Mineral. Soc., 2003, Part 132, no. 2, pp. 33–40.
Devyatykh, G.G., Karpov, Yu.A., Kovalev, I.D., et al., Additive Composition of Samples from the Exhibition-Collection of Substances of Special Purity. III. Simple Solid Substances from 3th and 4th Periods of Periodical Table of Elements, Vysokochistye Veshchestva, 1991, no. 2, pp. 22–32.
Petrov, T.G., On the Failing of Ability to Determine the Succession of Crystallization by Individual Characteristics of Mineral, Proc. All-Union Mineral. Soc., 1977, Part 106, no. 4, pp. 499–502.
Petrov, T.G., Theory of Information and Problems of Crystallogenesis, in sb. statei “protsessy rosta kristallov i plenok poluprovodnikov” (Coll. Papers’ Processes of Growth of Crystals and Films of Semiconductors’), Aleksandrov, L.N. and Borisova, L.A., Eds., Novosibirsk: 1970.
Petrov, T.G., About Complexity of Geochemical Systems from the Position of Theory of Information, Dokl. Akad. Nauk SSSR, 1970, vol. 191, no. 4, pp. 1094–1096.
Petrov, T.G. and Krasnova, N.I., R-slovar’-katalog khimicheskikh sostavov mineralov (R-Dictionary-Catalog of Chemical Compositions of Minerals), St. Petersburg: Nauka, 2010.
Shannon, C.E., A Mathematical Theory of Communication, Bell System Techn. J., 1948, vol. 27, pp. 623–656.
Moelwyn-Hudges, E.A., Physical Chemistry, London: Pergamon Press, 1961
Fano, R., Transmission of Information; A Statistical Theory of Communications, Cambridge: MIT Press, 1961.
Yaglom, A.M. and Yaglom, I.M., Probability and Information, Berlin: Springer Verlag, 1983.
Jaynes, E.T., Information Theory and Statistical Mechanics, Phys. Rev., 1957, vol. 106, no. 4, pp. 620–630; vol. 108, no. 2, pp. 171–190.
Traibus, M., Thermostatics and Thermodynamics, London, 1967.
Pelto, C.R., Mapping of Multicomponent Systems, J. Geol., 1954, vol. 62, no. 5, pp. 501–511.
Vistelius, A.B., Problems of Geochemistry and Information Measures, Sov. Geologiya, 1964, no. 12, pp. 5–26.
Buryakovskii, L.A., Entropy as Measure of Heterogeneity of Mountain Rocks, Sov. Geologiya, 1968, no. 3, pp. 135–138.
Logvinenko, N.V., Petrografiya osadochnykh porod (Petrography of Sedimentary Rocks), Moscow: Vysshaya Shkola, 1984.
Bekman, I.N., Informatika. Kurs lektsii (Informatics. Course of Lectures), Moscow: Mos. Gos. Univ., 2009.
Gordienko, V.V. and Petrov, T.G., Analysis of Processes of Formation of Rare Metal Granit Pegmatites with the Help of RHA Information Language, Proc. All-Union Mineral. Soc., 1981, Part 110, no. 5, pp. 546–558.
Petrov, T.G., Problems of Separation and Mixing in Inorganic Systems, Sb. statei “Geologiya”, (Coll. Papers “Geologiya”), Trofimov, V.T., Ed., 1995, vol. 2, pp. 181–186.
Gresens, R.L., Composition-Volume Relationships of Metasomatism, Chem. Geol., 1967, vol. 2, no. 1, pp. 47–65.
Petrov, T.G., The Way of Equal Brevities for Revealing Passive Components and Character of Behavior of Active Components in Geochemical Processes, Proc. All-Union Mineral. Soc., 1983, Part 112, no. 6, pp. 641–650.
Shurubor, Yu.V., About One Property of Geochemical System Complexity Measure, Dokl. Akad. Nauk SSSR, 1972, vol. 205, no. 2, pp. 453–456.
Le Maitre, R.W., The Chemical Variability of Some Common Igneous Rocks, J. Petrolog. 1976, vol. 17, pp. 589–637.
Spiridonov, E.M., Baksheev, I.A., Seredkin, M.V., et al., Gumbeities of Ural and Conjugated Rock Mineralization, Geolog. Rudn. Mestorozhd., 1998, vol. 40, no. 2, pp. 174–190.
Sobolev, A.P., Mezozoiskie granitoidy Severo-Vostoka SSSR i problemy ikh rudonosnosti (Mesozoic Granitoids of North-East of USSR and Problems of Their Ore-Bearingness), Moscow: Nauka, 1989.
Demograficheskii entsiklopedicheskii slovar’ (Demographic Encyclopaedic Dictionary), Moscow: Sov. Entsiklopediya, 1985.
Shvanov, V.N., Petrografiya peschanykh porod (Petrography of Sandy Rocks), Leningrad: Nedra, 1987.
Rossiya v tsifrakh. 2008 (Russia in Numbers-2008), Moscow, 2008.
Gini, C., I Fattori Demografici Dell’Evolucione Delle Nazioni, Torino, 1912.
Petrov, T.G., State of Information about Substance Composition of Geological Objects, Sov. Geologiya, 1976, no. 7, pp. 108–118.
Mazur, M., Kachestvennaya teoriya informatsii (A Quality Theory of Information), Warsaw: Widavnictvo Naukovo-Techniczne, 1970.
Efremova, S.V. and Stafeev, K.G., Petrokhimicheskie metody issledovaniya gornykh porod (Petrochemical Methods of Study of Mountain Rocks), Moscow: Nedra, 1985.
Moshkin, S.V., Shelemotov, A.S., Petrov, T.G., and Krasnova, N.I., “RETROS-2”—Program Complex for Treatment of Petrochemical Data, in Geokhimiya magmaticheskikh porod, (Geochemistry of Magmatic Rocks), Apatity: Karel. Nauchn. Tsentr Ross. Akad. Nauk, 2003.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © T.G. Petrov, 2012, published in Nauchno-Tekhnicheskaya Informatsiya, Seriya 2, 2012, No. 3, pp. 21–31.
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0005105512020045