to second order in the relaxation time (instead of the usual first order treatment) we expect to broaden even more the range of applicability of the effective theory, to be able to describe better those situations with large momentum-space anisotropies.

The limitations of the model put forward in this work are discussed in the last section, but it is worth mentioning them here. The model is phenomenological, it is valid only when the gauge fields can be treated classically, and only when the relaxation time approximation is valid. Moreover, the collision term is linear. We would like to stress that our approach is not new. The idea of obtaining a closure from a variational principle whose Lagrange multipliers are identified with macroscopic variables is at the heart of the so-called Extended Thermodynamic Theories (see e.g. [@extended]), which use as a variational principle the EMP. However, in most applications of this theory the EMP is only used to express $f$ in terms of the Lagrange multipliers [*but not*]{} to obtain their dynamics. In Refs. [@tanos; @anile; @tanos2; @tanos3; @muscato] the EMP was used to accomplish both tasks in the context of electron transport through mesoscopic semiconductors in the nonlinear and nonequilibrium 