the colorless and colored parts of $\mathbf{f}$:

f&= f\_0 \[fexp\]

f\^a = f\_0 (\^[a(1)]{}+ \_[ij]{}\^[(1)]{}p\^i p\^j \^[a(1)]{} + d\_[ef]{}\^a \^[e(1)]{} \^[f(1)]{}) \[fa\]

As discussed in the Introduction, this method, or very similar ones based on maximizing the entropy, have been used in different contexts to obtain closures for the distribution function, which resulted in effective models whose dynamics compared well with kinetic theory (see e.g. [@epvm; @prigo] for a broad perspective and [@tanos; @anile; @tanos2; @muscato; @tanos3; @linking; @christen; @christen2] for specific applications).

To obtain a dynamical model, we must now find the equation of motion of the Lagrange multipliers.

Equations of motion {#motion}
-------------------

The EPP described above has provided us with an expression for the distribution function $\mathbf{f}$ in terms of the reduced set of variables of the effective theory: the usual hydrodynamic variables $u^\mu$, $\rho$, the nonhydrodynamic tensor $\lambda_{\mu\nu}^{(1)}$ encoding the back reaction of $\mathbf{f}$ on the hydrodynamic modes, and the color fugacities $\zeta^{a(1)}$. This expression is given in Eq. (\[closfin\]).

The equations of motion for $u^\mu$, $\rho$ and $\zeta^{a(1)}$ are the conservation equations for $T^{\mu\nu}$ and $J^{a\mu}$, respectively. However, the conservation laws are not enough to fully determine the dynamics of the system, and an equation 