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

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: $$N(q-1)<1$$ . 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.