U$_{q}$ in Eq. (19) is expressed in terms of α (see Appendix B1), From Eqs. (18) and (61), U$_{q}$ and α are self-consistently determined as Equation (62) yields the specific heat given by The specific heat of harmonic oscillators was discussed in Ref. [19] with the use of un- normalized [5] and normalized MEMs [2]. Their expressions for the internal energy U$_{q}$ have rather complicated q dependence [see Eqs. (12) and (22) of Ref. [19]]. Equation (64) expresses the Dulong-Petit specific heat: C$_{BG}$ = k$_{B}$DN in the BG statistics, which is in agreement with Ref. [18]. The Tsallis entropy is given by Eq. (40) with The BG entropy in the limit of q = 1 . 0 is given by with For harmonic oscillators under consideration, we obtain (see Appendix B2) 2. Normal average U$_{q}$ = DN [ DN (1 − q ) + 1] α . (61) U$_{q}$ = DN β = k$_{B}$ DNT, (62) α = β 1 + DN (1 − q ) for 0 < q < 1 + 1 DN ≡ q$_{U}$. (63) C$_{q}$ = k$_{B}$DN. (64) c$_{q}$ = ν$_{q}$ ( Z$_{q}$ ) $^{1}$− $^{q}$, (65) ν$_{q}$ = DN (1 − q ) + 1 . (66) S$_{1}$ = NS (1) 1 , (67) S (1) 1 = k$_{B}$D [ ln ( 2 π hωβ ) + 1 ] . (68) ˜ Z$_{q}$ =      1 h DN [ 2 π ( $^{q}$− 1) ω ˜ α ] DN Γ ( 1 q$_{−}$ $_{1}$+1 ) Γ ( 1 q$_{−}$ $_{1}$+ DN +1 ) for 1 < q < 3 , 1 h DN ( 2 π ω ˜ α ) DN for q = 1 , 1 h DN [ 2 π $^{(1}$− q ) ω ˜ α ] DN Γ ( 1 1 $_{−}$q − DN ) Γ ( 1 1 $_{$_{−}$q}$) for q < 1 . (69) 12