Algebraic Representation of the Group of Havrda–Charvat–Daroczy Entropy Vectors in Nonextensive Statistical Mechanics
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An algebraic representation of the group of nonextensive, parameterized Havrda–Charvat–Daroczy entropy vectors that depend on three distributions is constructed. The composition law of conformally-generalized hypercomplex numbers is considered, and properties of a commutative, nonassociative algebra are derived. The exponential form of the number and functions of numbers with hyperbolic angles are presented.
Keywordsnonextensivity entropy group algebra geometry
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- 2.R. G. Zaripov, Principles of Non-Extensive Statistical Mechanics and The Geometry of Measures of Disorder and Order [in Russian], Publishing House of Kazan’ State Pedagogical University, Kazan’ (2010).Google Scholar
- 5.I. J. Taneja, Advances in Electronics and Electron Physics, 76, 327 (1989); accessible at http:/www.mtm.ufsc.br/~taneja/book.
- 6.R. G. Zaripov, New Measures and Methods in Information Theory [in Russian], Publishing House of Kazan’ State Pedagogical University, Kazan’ (2005).Google Scholar
- 13.R. G. Zaripov, J. Phys.: Conf. Ser., 394, 1 (2012).Google Scholar
- 15.R. G. Zaripov, in: Recent Problems in Field Theory 2005–2006 [in Russian], A. V. Aminova, ed., Publishing House of Kazan’ University (2007).Google Scholar