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We investigate the transverse momentum ($p_{\rm T}$) spectra of identifiedhadrons in minimum-bias proton-proton (pp) collisions at a centre-of-massenergy ($\sqrt{s}$) of 0.9, 2.76, 5.02, 7 and 13 TeV in the framework ofTsallis-blast wave (TBW) model. It is found that the model describes well theparticle spectra up to 10 GeV/c. The radial flow ($\langle \beta \rangle$)increases with the collision energy. The degrees of non-equilibrium ($q$) andthe Tsallis temperature parameter ($T$) show a similar behaviour, but with amuch weaker trend. With this dependence of the freeze-out parameters on thecollision energy, we evaluate $\langle \beta \rangle$, $T$ and $q$ in ppcollisions at $\sqrt{s}=$ 8 and 14 TeV and predict the particle spectra atthese two energies. Moreover, in order to investigate the multiplicitydependence of the freeze-out parameters, the TBW model is extended to thespectra at different charged-particle multiplicity classes in pp collisions at$\sqrt{s}=$ 7 and 13 TeV. It is observed that at both energies the radial flowincreases with the multiplicity while the degree of non-equilibrium shows anopposite behaviour, which is similar to that observed in proton-nucleus (pA)and nucleus-nucleus (AA) collisions at the Large Hadron Collider (LHC)energies. However, the Tsallis temperature parameter increases with themultiplicity, which is opposite to the trend in pA and AA collisions. Atsimilar multiplicities, the radial flow in pp collisions is stronger than thosein pA and AA collisions, indicating that the size of the colliding system hassignificant effects on the final state particle dynamics. Finally, we apply anadditional flow correction to the Tsallis temperature parameter and find thatthe doppler-corrected temperature parameter almost scales with the multiplicityin a uniform way, despite the difference in the colliding system and collisionenergy.

Collective expansion in pp collisions using the Tsallis statistics