basic plan we will follow is to divide relevant variables into colorless and colored pieces. Therefore, we parametrize $\mathbf{Z}$ as follows = + \^a \^a \[parz\] The quantities $\zeta^a$ can be identified with color fugacities $\zeta^a \equiv \mu^a/T$, where $\mu^a$ are the color chemical potentials needed to conserve color (see Eq. (\[13\])). We shall show later that the color chemical potentials must adjust to the flow of matter as well as to the evolving gauge fields in order to make the system globally colorless, resulting in a highly nontrivial dynamics for the system of colored particles and gauge fields. We will work to quadratic order in $\mathbf{Z}$, so we get

= + \^2 Using that \^a\^b = \^[ab]{} + K\^[ab]{}\_c \^c with K\^[ab]{}\_c (i C\_[abc]{}+ d\_[abc]{}) where $d_{abc}$ are the symmetric structure constants, we get \^2 = \^2 + \^a \^a + \^a \^a + \^a \^b d\^[ab]{}\_c \^c

Having $\mathbf{Z}$, we obtain

&= + \^a \^a +

### Currents, entropy production and collision term

To solve the variational problem we must express the currents and the entropy production in terms of $\mathbf{Z}$.

The shear tensor \^ = p\^p\^ reads \^ = p\^p\^\[shearfull\] where we have introduced the notation Dp 