where the bracket [ · ]$_{q}$ denotes the q average, Tr the trace and U$_{q}$ the q -averaged energy. The OLM-MEM yields the density matrix given by [6] with where [ x ]$_{+}$ = max( x, 0) and γ expresses a Lagrange multiplier. Although β is conventionally used for the relevant Lagrange multiplier, we employ γ to avoid a confusion with the inverse of physical temperature ( T = 1 /k$_{B}$β ). The Tsallis entropy defined by Eq. (1) is expressed in terms of c$_{q}$ by where c$_{q}$ is given by Eq. (10). Next we relate the Lagrange multiplier γ to the physical temperature T . It is an open problem how to define the physical temperature in conformity with the zeroth law of ther- modynamics in the nonextensive statistics [38]-[43]. Among several schemes proposed for defining the physical temperature [38]-[43], the method of Ref. [38] has been employed in this study. We assume that the physical temperature T is given by [38] (for details, see Appendix A, related discussions being also given in Sec. VB) which yields We may rewrite Eq. (11) as with ρ$_{q}$ = 1 X$_{q}$ [1 − (1 − q ) γ ( H − U$_{q}$ )] 1 / $^{(1}$− q ) + , (11) X$_{q}$ = Tr [1 − (1 − q ) γ ( H − U$_{q}$ )] 1 / $^{(1}$− q ) + , (12) S$_{q}$ = c$_{q}$ − 1 1 q , (13) 1 T = 1 c$_{q}$ ∂S$_{q}$ ∂U$_{q}$ = k$_{B}$ γ, (14) γ = 1 k$_{B}$ T = β. (15) ρ$_{q}$ = 1 Z$_{q}$ [1 − (1 − q ) α H ] 1 / $^{(1}$− q ) + , (16) Z$_{q}$ = Tr [1 − (1 − q ) αH ] 1 / $^{(1}$− q ) + , (17) α = β 1 + (1 − q ) βU$_{q}$ . (18) 5