C. The physical temperature VI. CONCLUDING REMARKS As mentioned in the introduction, there are several proposals in relating the Lagrange multiplier to the physical temperature even within the OLM-MEM [38]-[43]. In this paper, we have adopted the scheme proposed in Ref. [38]. One of the alternatives is to define the physical temperature by 1 /T = ∂S$_{q}$/∂U$_{q}$ [3], yielding for ideal gases (with the OLM-MEM), which is different from Eq. (14) by a factor of c$_{q}$ . Then the Lagrange multiplier is determined as and the energy is given by The expression for the specific heat becomes complex because c$_{q}$ in Eq. (110) is temperature dependent: Z$_{q}$ in c$_{q}$ has the temperature dependence through γ . Specific heats and entropies in nonextensive ideal gases and harmonic oscillators have been calculated by using the MEMs with the q - and normal averages and by the superstatistics. Obtained results of ideal gases are summarized in Table 1: those of harmonic oscillators are similarly given if we read DN/ 2 → DN . Our calculations have shown the followings: (i) The MEMs with the q - and normal averages are valid for 0 < q < q$_{U}$ and q$_{L}$ < q < ∞ , respectively, where q$_{U}$ = 1 + 1 /ηDN and q$_{L}$ = 1 − 1 / ( ηDN + 1), (ii) Energy and specific heat obtained by the q average coincide with those derived by the normal average and in the BG statistics, (iii) the Tsallis entropy obtained by the q - and normal averages are in fairly good agreement for q$_{L}$ < q < q$_{U}$ , (iv) the Tsallis entropy in the q -average shows the exponential N dependence: S$_{q}$/N ∼ e $^{(1}$− q ) NS (1) 1 for N (1 − q ) ≫ 1, which is quite different from that in the normal average: ˜ S$_{q}$/N ∼ 1 / ( q − 1) N for N ( q − 1) ≫ 1, and 18 1 T = ∂S$_{q}$ ∂U$_{q}$ = k$_{B}$γ c$_{q}$, (108) γ = 1 k$_{B}$T c$_{q}$ , (109) U$_{q}$ = DNk$_{B}$ T c$_{q}$ 2 . (110)