Abstract
The Abel entropy group and its matrix representation with the general law of nonextensive entropy composition and quadratic nonlinearity are defined. Four types of matrices for the corresponding parametrical entropies are given and geometries for their measures are determined. Algebraic representation of an entropy group is presented for this types of the general entropy classification in statistical thermodynamics of complex systems. The corresponding geometries are global Finsler ones. The well-known relations for the nonextensive entropies follow from the properties of the conformally generalized hypercomplex numbers.
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