Energy fluctuations and the ensemble equivalence in Tsallis statistics

Abstract

We investigate the general property of the energy fluctuation for the canonical ensemble in Tsallis statistics and the ensemble equivalence. By taking the ideal gas and the non-interacting harmonic oscillators as examples, we show that, when the particle number N is large enough, the relative fluctuation of the energy is proportional to 1/N in the new statistics, instead of square root of 1/N in Boltzmann-Gibbs statistics. Thus the equivalence between the microcanonical and the canonical ensemble still holds in Tsallis statistics.

6 pages, 21 references

References in corpus (2)

• Ion acoustic waves in the plasma with the power-law q-distribution in nonextensive statistics
• Constraining nonextensive statistics with plasma oscillation data

Cited by in corpus (8)

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• Specific heat and entropy of $N$-body nonextensive systems
• The minimal length uncertainty and the nonextensive thermodynamics
• Energy distribution and energy fluctuation in Tsallis statistics
• Thermodynamic stability criterion and fluctuation theory in nonextensive thermodynamics
• The entropy in finite $N$-unit nonextensive systems: the ordinary average and $q$-average
• Thermodynamic relations and fluctuations in the Tsallis statistics
• Relation between the escort average in microcanonical ensemble and the escort average in canonical ensemble in the Tsallis statistics