Equilibrium statistical mechanics for incomplete nonextensive statistics

Abstract

The incomplete nonextensive statistics in the canonical and microcanonical ensembles is explored in the general case and in a particular case for the ideal gas. By exact analytical results for the ideal gas it is shown that taking the thermodynamic limit, with $z=q/(1-q)$ being an extensive variable of state, the incomplete nonextensive statistics satisfies the requirements of equilibrium thermodynamics. The thermodynamical potential of the statistical ensemble is a homogeneous function of the first degree of the extensive variables of state. In this case, the incomplete nonextensive statistics is equivalent to the usual Tsallis statistics. If $z$ is an intensive variable of state, i.e. the entropic index $q$ is a universal constant, the requirements of the equilibrium thermodynamics are violated.

7 pages

References in corpus (4)

• Microcanonical Ensemble Extensive Thermodynamics of Tsallis Statistics
• Extensive statistical mechanics based on nonadditive entropy: Canonical ensemble
• Possible canonical distributions for finite systems with nonadditive energy
• Inherent correlations between thermodynamics and statistic physics in extensive and nonextensive systems