content_image/347176.jpg content_image/347177.jpg content_image/347178.jpg content_image/347181.jpg content_image/347182.jpg content_image/347179.jpg content_image/347180.jpg content_image/347183.jpg
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 

<img src='content_image/347176.jpg'>

<img src='content_image/347177.jpg'>

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). 

<img src='content_image/347178.jpg'>

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 

<img src='content_image/347181.jpg'>

<img src='content_image/347182.jpg'>

<img src='content_image/347179.jpg'>

<img src='content_image/347180.jpg'>

<img src='content_image/347183.jpg'>

