title: Specific heat and entropy of N-body nonextensive systems.
abstract: 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.
authors.affiliation: Department of Physics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan. hideohasegawa@goo.jp
authors.forename: Hideo
authors.initials: H
authors.lastname: Hasegawa