Comparing linear and nonlinear hydrodynamical models for charge transport in graphene based on the Maximum Entropy Principle

Two hydrodynamical models for charge transport in graphene are presented. They are deduced as moment equations of the semiclassical Boltzmann equation with the needed closure relations obtained by resorting to the Maximum Entropy (Principle Jaynes, 1957; Müller and Ruggeri, 1998; Jou et al., 1993; Mascali and Romano, 2005). The models differ in the choice of the moments to assume as basic field variables. Both linear and nonlinear closure relations are analyzed. A comparison is performed with the results given by directly solving the transport equation through the method in Romano et al. (2015) and Coco et al. (2016). It has been found out that it is crucial to include the deviatoric part of the stress tensor. At the same time, it appears that the differences in the results between the linear and nonlinear models are not relevant.