Thermo-Statistical description of the Hamiltonian non extensive systems: The reparametrization invariance

In the present paper we continue our reconsideration about the foundations for a thermostatistical description of the called Hamiltonian nonextensive systems (see in cond-mat/0604290). After reviewing the selfsimilarity concept and the necessary conditions for the ensemble equivalence, we introduce the reparametrization invariance of the microcanonical description as an internal symmetry associated with the dynamical origin of this ensemble. Possibility of developing a geometrical formulation of the thermodynamic formalism based on this symmetry is discussed, with a consequent revision about the classification of phase-transitions based on the concavity of the Boltzmann entropy. The relevance of such conceptions are analyzed by considering the called Antonov isothermal model.