U$_{q}$ is expressed by with where we adopt the relation: c$_{q}$ = ( X$_{q}$ ) $^{1}$− q = ν$_{q}$ ( Z$_{q}$ ) $^{1}$− $^{q}$. In the original MEM with the normal average [1]  we impose the constraints given by (tildes are attached to quantities relevant to the normal average) where the bracket 〈·〉 q expresses the normal average and ˜ U$_{q}$ the normal-averaged energy. The original MEM [1  24] yields the density matrix give by with where ˜ γ denotes a Lagrange multiplier. The Tsallis entropy is expressed by with We assume that the physical temperature T is given by [38] (for a detailed discussion  see Appendix A) U$_{q}$ = 1 ν$_{q}$Z$_{q}$ Tr { [1 − (1 − q ) αH ] q/ $^{(1}$− q ) + H }   (19) ν$_{q}$ = [1 + (1 − q ) βU$_{q}$ ]   (20) 1 = Tr ˜ ρ$_{q}$  (21) ˜ U$_{q}$ = 〈 H 〉 q = Tr { ˜ p$_{q}$H }   (22) ˜ p$_{q}$ = 1 ˜ X$_{q}$ [ 1 − ( q − 1)˜ γ ( H − ˜ U$_{q}$ )] 1 / ( $^{q}$− 1) +   (23) ˜ X$_{q}$ = Tr [ 1 − ( q − 1)˜ γ ( H − ˜ U$_{q}$ )] 1 / ( $^{q}$− 1) +   (24) S$_{q}$ = ˜ c$_{q}$ − 1 1 q   (25) ˜ c$_{q}$ = Tr (˜ ρ$_{q}$ ) $^{q}$. (26) 1 T = 1 ˜ c$_{q}$ ∂S$_{q}$ ∂ ˜ U$_{q}$ = q k$_{B}$ ˜ γ  (27) 6 B. Original MEM with the normal average