https://doi.org/10.1140/epjb/s10051-023-00481-7
Regular Article - Statistical and Nonlinear Physics
Thermodynamic quantities of independent harmonic oscillators in microcanonical and canonical ensembles in the Tsallis statistics
Department of Food and Nutrition, Koriyama Women’s University, 963-8503, Koriyama, Fukushima, Japan
Received:
5
September
2022
Accepted:
8
January
2023
Published online:
27
January
2023
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: 
. The condition does not appear in the microcanonical ensemble.The entropies are q-dependent in the canonical ensemble, and are not q-dependent in the microcanonical ensemble. For , this difference in entropy is quite small, and the entropy in the canonical ensemble does not differ from the entropy in the microcanonical ensemble substantially.
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