### 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.

Original language | English |
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Pages (from-to) | 372-378 |

Number of pages | 7 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 375 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 17 2011 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Equilibrium statistical mechanics for incomplete nonextensive statistics.** / Parvan, A. S.; Bíró, T.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 375, no. 3, pp. 372-378. https://doi.org/10.1016/j.physleta.2010.12.022

}

TY - JOUR

T1 - Equilibrium statistical mechanics for incomplete nonextensive statistics

AU - Parvan, A. S.

AU - Bíró, T.

PY - 2011/1/17

Y1 - 2011/1/17

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78650868766&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650868766&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2010.12.022

DO - 10.1016/j.physleta.2010.12.022

M3 - Article

AN - SCOPUS:78650868766

VL - 375

SP - 372

EP - 378

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 3

ER -