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

Abstract

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.

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

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• Thermodynamic properties and transport coefficients of QCD matter within the non-extensive Polyakov-Nambu-Jona-Lasinio model
• Fractal surfaces from simple arithmetic operations
• Quantum Mechanics and the Principle of Least Radix Economy
• The $p\lambda n$ fractal decomposition: Nontrivial partitions of conserved physical quantities
• The nonextensive statistical ensembles with dual thermodynamic interpretations
• The Phase Space Elementary Cell in Classical and Generalized Statistics
• Diagrammatic approach to cellular automata and the emergence of form with inner structure
• Microcanonical equations for the Tsallis entropy
• Thermodynamic properties of the solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation
• Irreversibility and maximum generation in $\kappa$-generalized statistical mechanics
• Maximum entropy generation in open systems: the Fourth Law?
• The thermodynamic hamiltonian for open systems