  The mid-rapidity transverse-momentum spectra of charmed meson in Pb-Pb and
pp($\overline{\text{p}}$) collisions are analyzed by Tsallis-Pareto
distribution derived from non-extensive statistics. We perform uniform
descriptions for both small and large systems over a wide range of collision
energy and hadron transverse momentum. By establishing the relation between the
event multiplicity and the Tsallis parameters, we observe that there is
significant linearity between thermal temperature and Tsallis-q parameter in
Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV and 5.02 TeV. And the slope of
the T $-$ (q - 1) parameter is positively correlated with the hadron mass. In
addition, the charm mesons have higher thermal temperature than the light
hadrons at the same q - 1, indicating that charmed flavor requires a higher
temperature to achieve the same degree of non-extensive as light flavors in the
heavy-ion collision. The same fit is performed to the transverse momentum
spectra of charmed meson in pp($\overline{\text{p}}$) collision over a large
energy range with Tsallis-Pareto distribution. It is found that the thermal
temperature increases with system energy while the q parameter shows a
saturated 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 are
found to approach the pp($\overline{\text{p}}$) limit, which suggests that less
medium effect and more in similarity with pp($\overline{\text{p}}$) collisions
are found in more peripheral heavy-ion collisions.
