Non-extensive Statistics and a Systematic Study of Meson-Spectra at LHC Energy $\sqrt{s_{NN}}=2.76$ TeV

The transverse momentum spectra of secondary pions and kaons, produced in $P+P$ and various central $Pb+Pb$ collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC, have been analyzed systematically with an approach based on Tsallis non-extensive statistics. The analytical results have been utilized to determine some of the very important thermodynamical parameters bearing characteristic signatures of the partonic medium produced in such collisions.