method {#sumclos}

For clarity, we now briefly summarize the main logical steps followed to obtain the closure for $\mathbf{f}$.

From a linear transport equation, we set up the variational problem given in Eqs. (\[varia\]). The solution to these equations gives the distribution function that extremizes the production of entropy subject to the constraints that the conserved currents take on known values. Using the expressions for the stress tensor, the color currents and the entropy production given in Eqs. (\[shearfull\]), (\[jdfull\]) and (\[entaux\]), respectively, together with the integrability conditions for the collision term, Eqs. (\[i0aux\]) and (\[iaaux\]), the variational equations become Eqs. (\[variat1\]) and (\[variat2\]).

We then expand the Lagrange multipliers and the nonequilibrium correction $\mathbf{Z}$ in powers of the relaxation time $\tau$ (Eq. (\[zetas2nd\])), and solve the variational equations to second order in $\tau$. The result is an expression for the correction $\mathbf{Z}$ in terms of the Lagrange multipliers, which is given by Eqs. (\[zeta10\]) and (\[zeta20\]). From these equations, we can express the shear tensor and the color currents in terms of the Lagrange multipliers, obtaining Eqs. (\[pi1aux\]), (\[j1a\]), (\[piphys\]) and (\[j2htot\]).

The distribution function then reads

&=f\_0\
&+ f\_0

\[closfin\] For convenience, we denote by $f$ and $f^a$ 