Nonextensive statistical mechanics: Equivalence between dual entropy and dual probabilities

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The concept of duality of probability distributions constitutes a fundamental "brick" in the solid framework of nonextensive statistical mechanics-the generalization of Boltzmann-Gibbs statistical mechanics under the consideration of the q-entropy. The probability duality is solving old-standing issues of the theory, e.g., it ascertains the additivity for the internal energy given the additivity in the energy of microstates. However, it is a rather complex part of the theory, and certainly, it cannot be trivially explained along the Gibb's path of entropy maximization. Recently, it was shown that an alternative picture exists, considering a dual entropy, instead of a dual probability. In particular, the framework of nonextensive statistical mechanics can be equivalently developed using q-and 1/q-entropies. The canonical probability distribution coincides again with the known q-exponential distribution, but without the necessity of the duality of ordinary-escort probabilities. Furthermore, it is shown that the dual entropies, q-entropy and 1/q-entropy, as well as, the 1-entropy, are involved in an identity, useful in theoretical development and applications.

Original languageEnglish (US)
Article number594
Issue number6
StatePublished - Jun 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering


  • Escort probability
  • Kappa distributions
  • Nonextensive statistical mechanics
  • Q-entropy


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