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We expand the Tsallis distribution in a Taylor series of powers of (q-1),where q is the Tsallis parameter, assuming q is very close to 1. This helps instudying the degree of deviation of transverse momentum spectra and otherthermodynamic quantities from a thermalized Boltzmann distribution. Afterchecking thermodynamic consistency, we provide analytical results for theTsallis distribution in the presence of collective flow up to the first orderof (q-1). The formulae are compared with the experimental data.

Radial Flow in Non-Extensive Thermodynamics and Study of Particle Spectra at LHC in the Limit of Small $(q-1)$