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The mid-rapidity transverse-momentum spectra of charmed meson in Pb-Pb andpp($\overline{\text{p}}$) collisions are analyzed by Tsallis-Paretodistribution derived from non-extensive statistics. We perform uniformdescriptions for both small and large systems over a wide range of collisionenergy and hadron transverse momentum. By establishing the relation between theevent multiplicity and the Tsallis parameters, we observe that there issignificant linearity between thermal temperature and Tsallis-q parameter inPb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV and 5.02 TeV. And the slope ofthe T $-$ (q - 1) parameter is positively correlated with the hadron mass. Inaddition, the charm mesons have higher thermal temperature than the lighthadrons at the same q - 1, indicating that charmed flavor requires a highertemperature to achieve the same degree of non-extensive as light flavors in theheavy-ion collision. The same fit is performed to the transverse momentumspectra of charmed meson in pp($\overline{\text{p}}$) collision over a largeenergy range with Tsallis-Pareto distribution. It is found that the thermaltemperature increases with system energy while the q parameter shows asaturated trend and stops at pp($\overline{\text{p}}$) limit, q - 1 = 0.142$\pm$ 0.010. Meanwhile, the results of most peripheral Pb-Pb collisions arefound to approach the pp($\overline{\text{p}}$) limit, which suggests that lessmedium effect and more in similarity with pp($\overline{\text{p}}$) collisionsare found in more peripheral heavy-ion collisions.

Non-extensive statistical distributions of charmed meson production in Pb-Pb and pp($\overline{\text{p}}$) collisions