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

The self-consistency of a thermodynamical theory for hadronic sys- tems based on the non-extensive statistics is investigated. We show that it is possible to obtain a self-consistent theory according to the asymptotic bootstrap principle if the mass spectrum and the energy density increase q-exponentially. A direct consequence is the existence of a limiting effective temperature for the hadronic system. We show that this result is in agreement with experiments.