A non self-referential expression of Tsallis' probability distribution function

Abstract

The canonical probability distribution function (pdf) obtained by optimizing the Tsallis entropy under the linear mean energy constraint (first formalism) or the escort mean energy constraint (third formalism) suffer self-referentiality. In a recent paper [Phys. Lett. A {\bf335} (2005) 351-362] the authors have shown that the pdfs obtained in the two formalisms are equivalent to the pdf in non self-referential form. Based on this result we derive an alternative expression, which is non self-referential, for the Tsallis distributions in both first and third formalisms.

3 pages

References in corpus (9)

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• Deformed exponentials and logarithms in generalized thermostatistics
• Deformed logarithms and entropies
• Equivalence of the four versions of Tsallis statistics
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• Equivalence among different formalisms in the Tsallis entropy framework
• Affinity-based extension of non-extensive entropy and statistical mechanics
• Scaled Bregman divergences in a Tsallis scenario
• Scaling property and the generalized entropy uniquely determined by a fundamental nonlinear differential equation
• Deformed Statistics Free Energy Model for Source Separation using Unsupervised Learning
• The Boltzmann temperature and Lagrange multiplier