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

• Published in: The European physical journal. B, Condensed matter physics Vol. 96; no. 1
• Main Author: Ishihara, Masamichi
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2023; Springer; Springer Nature B.V
• Subjects: Complex Systems; Condensed Matter Physics; Entropy; Fluid- and Aerodynamics; Harmonic oscillators; Physics; Physics and Astronomy; Quantum statistics; Regular Article - Statistical and Nonlinear Physics; Solid State Physics; Statistics; Thermodynamics
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/s10051-023-00481-7

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 ) < 1 . 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 N ( q - 1 ) < 1 , 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. Graphic abstract