Nonextensive Statistical Mechanics

8.2 Frequently Asked Questions 3254030ln W Nln W 1201010 20 30 40 50 60 70 80 90 100NFig. 8.3 All one-particle W 1 states (W 1 = 1, 2, 3, ...) are assumed nondegenerate. We consider theN-particle case assuming no interaction energy between the particles. W (MB)N= W1 N , N > 0(blackcurve); W (FD) WN= 1!N!(W ,0< N ≤ W 1−N)! 1 (red curves); W (BE)N= (N+W1−1)!N!(W 1−1)!, N > 0(blue curves).N = 20, 50, 100, 1000, 100, 000. In the present scale, the FD and BE curves for N = 100, 000appear superimposed. In the limit N →∞and W 1 →∞with N/W 1 → 0, W (FD)Nand W (BE)Ncollapse onto the W (MB)Nresult; they both satisfy W N ∝ (W 1 /N) N .109876543211 2 3 4 5 6 7 8 9 10Nlnq WNFig. 8.4 N-dependence ofln q W 1,whereW N = W 1 N ρ (ρ>0) with q = 1 − 1 (ρ = 2 henceρlnq = 1/2; W 1 > 1, N ≥ 1). lim1−1/ρ W NN→∞ ln 1−1/ρ W 1= W 1/ρ1N, which asymptotically approaches NW 1/ρ1 −1ln Win the limit W 1 →∞. Under the same conditions lim NN→∞ ln W 1approaches unity, ∀N.Blue(red)set of curves for q = 1/2 (forq = 1), with W 1 = 20, 50, 100, 1000, 100, 000 from top to bottom.lnq WNBlack curves: = N for q = 1 − 1/ρ, andln q W 1= 1forq = 1.lnq WNln q W 1