Nonequilibrium distribution function and generalized hydrodynamics for independent electrons from an entropy production rate principle

The quasi-stationary nonequilibrium distribution function of an independent electron gas interacting with a medium, which is at local thermal equilibrium, can be obtained by entropy production rate minimization, subject to constraints of fixed moments. The approach serves as a closure of the associated generalized hydrodynamic equations of the electron gas for an arbitrary number of moments, and provides an access to far-from-equilibrium transport with nonlinear current-voltage behavior. Furthermore, the method turns out to be particularly useful for a description of semi-classical transport in mesoscopic (low-dimensional) electric conductors, because macroscopic contacts can be taken into account in a natural way. Copyright (C) EPLA, 2010