Possible connection of the generalized thermostatistics with a scale invariant statistical thermodynamics

A conjecture is presented on the possibility that the q-generalized statistical thermodynamics proposed by Tsallis may refer to scale invariant statistical mechanics. This scale symmetry is introduced by means of a fractal canonical ensemble, constructed by replicas of the same system at different scales. In this way, the Tsallis distribution of energy is derived from a renormalization of the Boltzmann-Gibbs distribution. Such an ensemble could be an appropriate description of systems with hierarchical structures. In particular, it might be useful in studying thermodynamics systems with a fractal structure in the phase-space. (C) 1997 Elsevier Science B.V.