  The Tsallis distribution has been used recently to fit the transverse
momentum distributions of identified particles by the STAR and PHENIX
collaborations at the Relativistic Heavy Ion Collider and by the ALICE and CMS
collaborations at the Large Hadron Collider. Theoretical issues are clarified
concerning the thermodynamic consistency of the Tsallis distribution in the
particular case of relativistic high energy quantum distributions. An improved
form is proposed for describing the transverse momentum distribution and fits
are presented together with estimates of the parameter $q$ and the temperature
$T$.
