Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space

We develop a generalized theory of (meta)equilibrium statistical mechanics ill the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, Our approach leads naturally to Boltzmann-Gibbs standard thermostatistics while, in the latter, Tsallis thermostatistics is straightforwardly obtained as the most appropriate formalism. We first focus on the microcanonical ensemble stressing the importance of the limit t -> infinity oil the form of the microcanonical measure. Interestingly, this approach leads to interpret the entropic index q as the box-counting dimension of the (microcanonical) phase space when fractality is considered. (c) 2005 Elsevier B.V. All rights reserved.