content_image/355413.jpg content_image/355414.jpg content_image/355415.jpg content_image/355416.jpg content_image/355417.jpg content_image/355418.jpg content_image/355419.jpg content_image/355420.jpg content_image/355421.jpg
U$_{q}$ is expressed by 

with 

where we adopt the relation: c$_{q}$ = ( X$_{q}$ ) $^{1}$− q = ν$_{q}$ ( Z$_{q}$ ) $^{1}$− $^{q}$. 

## B. Original MEM with the normal average 

<img src='content_image/355413.jpg'>

<img src='content_image/355414.jpg'>

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) 

<img src='content_image/355415.jpg'>

<img src='content_image/355416.jpg'>

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 

<img src='content_image/355417.jpg'>

<img src='content_image/355418.jpg'>

where ˜ γ denotes a Lagrange multiplier. The Tsallis entropy is expressed by 

with 

<img src='content_image/355419.jpg'>

<img src='content_image/355420.jpg'>

We assume that the physical temperature T is given by [38] (for a detailed discussion, see Appendix A) 

<img src='content_image/355421.jpg'>

