Where the Tsallis Statistic is valid?

Abstract

In the present paper are analysed the conditions for the validity of the Tsallis Statistics. The same have been done following the analogy with the traditional case: starting from the microcanonical description of the systems and analysing the scaling properties of the fundamental macroscopic observables in the Thermodynamic Limit. It is shown that the Generalized Legendre Formalism in the Tsallis Statistic only could be applied for one special class of the bordering systems, those with non exponential growth of the accessible states density in the thermodynamic limit and zero-order divergency behavior for the fundamental macroscopic observables, systems located in the chaos threshold.