A Generalization of Tsallis' Non-Extensive Entropy and Energy Landscape Transformation Functions

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This article extends the non-extensive entropy of Tsallis and uses this entropy to model an energy producing system in an absorbing heat bath. This modified non-extensive entropy is superficially identical to the one proposed by Tsallis, but also incorporates a ''hidden'' parameter that provides greater flexibility for modeling energy constraints. This modified non-extensive entropy also leads to a more generalized family of energy transformation functions and also exhibits the structural scale invariance properties described in a previous article. This energy transformation also provides a more natural mechanism by which arbitrary power-law distributions can be stated in exponential form.