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The quasi-stationary nonequilibrium distribution function of an independentelectron gas interacting with a medium, which is at local thermal equilibrium,can be obtained by entropy production rate minimization, subject to constraintsof fixed moments. The result is not restricted to the region near equilibrium(linear response) and provides a closure of the associated generalizedhydrodynamic equations of the electron gas for an arbitrary number of moments.Besides an access to far from equilibrium states, the approach provides auseful description of semi-classical transport in mesoscopic conductors,particularly because macroscopic contacts can be naturally taken into account.

Steady-state distribution function for a gas of independent electrons far from equilibrium