Self-consistency in non-extensive thermodynamics of highly excited hadronic states

► This work extends the self-consistency principle proposed by Hagedorn to the non-extensive hadronic systems. ► It is shown that the self-consistency condition can be satisfied in the non-extensive thermodynamics. ► The asymptotic form of the mass spectrum and of the density of states are obtained through the self-consistency condition. ► It is shown that a limiting effective temperature exists for highly excited hadronic systems.