Study of invariance of nonextensive statistics under the uniform energy spectrum translation

A.S. Parvan

Physica A: Statistical Mechanics and its Applications, 2022, vol. 588, issue C

Abstract: The general formalisms of the q-dual statistics, the Boltzmann–Gibbs statistics, and three versions of the Tsallis statistics known as Tsallis-1, Tsallis-2, and Tsallis-3 statistics have been considered in the canonical ensemble. We have rigorously proved that the probability distribution of the Tsallis-1 statistics is invariant under the uniform energy spectrum translation at a fixed temperature. This invariance demonstrates that the formalism of the Tsallis-1 statistics is consistent with the fundamentals of the equilibrium statistical mechanics. The same results we have obtained for the probability distributions of the Tsallis-3 statistics, Boltzmann–Gibbs statistics, and q-dual statistics. However, we have found that the probability distribution of the Tsallis-2 statistics, the expectation values of which are not consistent with the normalization condition of probabilities, is indeed not invariant under the overall shift in energy as expected.

Keywords: Nonextensive statistics; Tsallis statistics; q-dual statistics (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:588:y:2022:i:c:s0378437121008293

DOI: 10.1016/j.physa.2021.126556

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