content_image/353338.jpg content_image/353339.jpg content_image/353340.jpg content_image/353341.jpg content_image/353342.jpg content_image/353343.jpg
coefficients which appear in the exponential are calculated in the following way, 

<img src='content_image/353338.jpg'>

and 

<img src='content_image/353339.jpg'>

The chemical potential µ$_{q}$ is decomposed to µ$_{q}$ = 1 $_{3}$µ$_{B}$ + Sµ$_{S}$ + · · · . From the fugacity definition, it is worth to keep in mind that βµ$_{q}$ → 1 T µ$_{q}$ . In the case of massless flavors, we have 

<img src='content_image/353340.jpg'>

and 

<img src='content_image/353341.jpg'>

where ( · · · ) indicates the neglected massive flavors. 

The grand canonical ensemble for the adjoint gluons can be calculated in a similar way to that one done in calculating the fundamental quark and antiquark grand canonical ensemble in the functional integral representation (see for instance Eq.(15)). For the sake of simplicity, the axial gauge is considered and the result is manifestly gauge invariant [55]. In the axial gauge, the canonical partition function for a gas of adjoint gluons reads 

where the action is given by 

<img src='content_image/353342.jpg'>

<img src='content_image/353343.jpg'>

