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

## TL;DR

This paper develops fluid-dynamic models for electron transport in graphene near a Dirac point, derived from kinetic equations using entropy minimization and specific assumptions, to better understand quantum transport phenomena.

## Contribution

It introduces a novel approach to derive fluid models from kinetic equations for graphene electron transport via entropy minimization under new assumptions.

## Key findings

- Derived fluid-dynamic models from kinetic equations for graphene.
- Closed moment equations using minimum entropy principle.
- Explicit closure formulas under specific assumptions.

## Abstract

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 ($\hbar\ll 1$), and two further hypothesis, namely Low Scaled Fermi Speed (LSFS) and Strongly Mixed State (SMS), which allow us to explicitly compute the closure.