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

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 -> 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.