Quantum vibrational partition function in the non-extensive Tsallis framework

The Minimal Length Uncertainty and the Nonextensive Thermodynamics

“…For T = 2, as it is shown in Fig. 1, we have p * n > p n for small n and p n > p * n for large n. Moreover, these results can be compared with those in the absence of the minimal length scale [58]. Indeed, for small quantum numbers we have p n > p n (γ = 0) and p * n > p * n (γ = 0).…”

“…We also compare our results with the corresponding quantities in the absence of minimal length [58] and with the Boltzmann-Gibbs thermodynamics. Note that the black-body radiation in Tsallis statistics and in the presence of the minimal length can also be treated using this model.…”

“…which Z 0 ≡ Z vib,q (γ = 0 = β) is the vibrational partition function of quantum harmonic oscillator in the absence of minimal length scale [58], namely…”

“…where U 0 ≡ U (γ = 0) is the internal energy corresponds to the absence of the minimal length scale which is given by [58] …”

“…, which is shown that the Tsallis entropy is more stable [57]. Recently, some authors have investigated the exact vibrational partition function for quantum nonextensive harmonic oscillator [58]. They showed that for all T and 1 < q < 2 the inequality Z > Z * holds and Z − Z * increases as q and T grow up where Z and T represent the partition function and temperature, respectively.…”