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 \(q\rightarrow 1/q\). 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.

中文翻译：

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现象学Tsallis分布与q对偶统计量的横向动量分布的等价性

在目前的工作中，我们发现现象学的Tsallis分布（如今主要用于描述高能pp碰撞中测得的强子的横向动量分布）是否符合统计力学的基础（如果它属于q） -双重非广泛统计，而不是Tsallis统计。我们根据熵参数\（q \ rightarrow 1 / q \）的乘法变换后从Tsallis熵获得的q对偶熵定义了q对偶统计量。我们发现现象学的Tsallis分布等于q的横向动量分布-零项近似中的双重统计量。由于正确地定义了q对偶统计量，因此它在现象学Tsallis分布与热力学第二定律之间提供了正确的联系。