Some fluid-dynamic models for quantum electron transport in graphene via entropy minimization

We derive some fluid-dynamic models for electron transport near a Dirac point in graphene. We start from a kinetic model constituted by a set of spinorial Wigner equations, we make suitable scalings (hydrodynamic or diffusive) of the model and we build moment equations, which we close through a minimum entropy principle. In order to do this we make some assumptions: the usual semiclassical approximation ($\mathrm{\hslash }\ll 1$), and two further hypothesis, namely Low Scaled Fermi Speed (LSFS) and Strongly Mixed State (SMS), which allow us to explicitly compute the closure.