  The Tsallis distribution has been used recently to fit the transverse
momentum distributions of identified particles by the STAR collaboration
\cite{Abelev:2006cs} at the Relativistic Heavy Ion Collider and by the ALICE
\cite{Aamodt:2011zj} and CMS \cite{Khachatryan:2011tm} 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 $T$.
