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

Physics – Condensed Matter – Statistical Mechanics

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14 pages, 1 table, no figures. Accepted for publication in Physica A

Scientific paper

10.1016/j.physa.2005.07.006

We develop a generalized theory of (meta)equilibrium statistical mechanics in 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 $t \to \infty$ on 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.

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