arXiv:1002.4052v5 [cond-mat.stat-mech] 12 Aug 2010 Specific heat and entropy of N -body nonextensive systems Hideo Hasegawa ∗ Department of Physics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan (Dated: November 5, 2018) We have studied finite N -body D -dimensional nonextensive ideal gases and harmonic oscillators, by using the maximum-entropy methods with the q - and normal averages ( q : the entropic index). The validity range, specific heat and Tsallis entropy obtained by the two average methods are compared. Validity ranges of the q - and normal averages are 0 < q < q$_{U}$ and q > q$_{L}$ , respectively, where q$_{U}$ = 1 + ( ηDN ) − $^{1}$, q$_{L}$ = 1 − ( ηDN + 1) − 1 and η = 1 / 2 ( η = 1) for ideal gases (harmonic oscillators). The energy and specific heat in the q - and normal averages coincide with those in the Boltzmann-Gibbs statistics, although this coincidence does not hold for the fluctuation of energy. The Tsallis entropy for N | q − 1 | ≫ 1 obtained by the q -average is quite different from that derived by the normal average, despite a fairly good agreement of the two results for | q − 1 | ≪ 1. It has been pointed out that first-principles approaches previously proposed in the superstatistics yield additive N -body entropy ( S ( N ) = NS $^{(1)}$) which is in contrast with the nonadditive Tsallis entropy. PACS numbers: 05.70.-a, 05.70.Ce, 05.20.Gg, 51.30.+i Abstract ∗ hideohasegawa@goo.jp 1