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arXiv · 1910.13840

Equivalence of the phenomenological Tsallis distribution to the transverse momentum distribution of $q$-dual statistics

A. S. Parvan
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Abstract

In the present work, we have found that the phenomenological Tsallis distribution (which nowadays is largely used to describe the transverse momentum distributions of hadrons measured in $pp$ collisions at high energies) is consistent with the basis of the statistical mechanics if it belongs to the $q$-dual nonextensive statistics instead of the Tsallis one. We have defined the $q$-dual statistics based on the $q$-dual entropy which was obtained from the Tsallis entropy under the multiplicative transformation of the entropic parameter $q\to 1/q$. We have found that the phenomenological Tsallis distribution is equivalent to the transverse momentum distribution of the $q$-dual statistics in the zeroth term approximation. Since the $q$-dual statistics is properly defined, it provides a correct link between the phenomenological Tsallis distribution and the second law of thermodynamics.

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A. S. Parvan. 2019-10-29. Equivalence of the phenomenological Tsallis distribution to the transverse momentum distribution of $q$-dual statistics. https://doi.org/10.1140/epja%2Fs10050-020-00117-9

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