## Abstract

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 language | English (US) |
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Article number | 594 |

Journal | Entropy |

Volume | 22 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1 2020 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

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

## Keywords

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