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Generalized algebra within a nonextensive statistics. (English) Zbl 1125.82300

Summary: By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators: addition, subtraction, product and division, are generalized. The properties of the generalized operators are investigated. Some standard properties are preserved, e.g. associativity, commutativity and existence of neutral elements. On the contrary, the distributivity law and the opposite element are no more universal within the generalized algebra.

MSC:

82C03 Foundations of time-dependent statistical mechanics
80A05 Foundations of thermodynamics and heat transfer
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