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Thermodynamic quantities of independent harmonic oscillators in microcanonical and canonical ensembles in the Tsallis statistics

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  • Masamichi Ishihara

    (Koriyama Women’s University)

Abstract

We study the energy and the entropies of N independent harmonic oscillators in the microcanonical and the canonical ensembles in the Tsallis classical and the Tsallis quantum statistics of entropic parameter q, where N is the number of the oscillators and the value of q is larger than one. The energy and the entropies are represented with the physical temperature, and the well-known expressions are obtained for the energy and the Rényi entropy. The difference between the microcanonical and the canonical ensembles is the existence of the condition for N and q in the canonical ensemble: $$N(q-1)

Suggested Citation

  • Masamichi Ishihara, 2023. "Thermodynamic quantities of independent harmonic oscillators in microcanonical and canonical ensembles in the Tsallis statistics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(1), pages 1-12, January.
    • Handle: RePEc:spr:eurphb:v:96:y:2023:i:1:d:10.1140_epjb_s10051-023-00481-7
    DOI: 10.1140/epjb/s10051-023-00481-7
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    References listed on IDEAS

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    1. Abe, Sumiyoshi, 2001. "Heat and entropy in nonextensive thermodynamics: transmutation from Tsallis theory to Rényi-entropy-based theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 417-423.
    2. Toral, Raúl, 2003. "On the definition of physical temperature and pressure for nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 209-212.
    3. Masamichi Ishihara, 2022. "Thermodynamics of the independent harmonic oscillators with different frequencies in the Tsallis statistics in the high physical temperature approximation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(3), pages 1-10, March.
    4. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
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