Hydrodynamical models for charge transport in graphene based on the Maximum Entropy Principle: the case of moments based on energy powers

Hydrodynamical models for charge transport in graphene can be obtained as moment equations of the semiclassical Boltzmann equation in which the needed closure relations are obtained by resorting to the Maximum Entropy Principle (Jaynes 1957; Müller and Ruggeri 1998; Mascali and Romano 2005; Jou and Lebon 2010). Several choices of the weight functions defining the moments can be made. The aim of this paper is analyzing the case in which the moments are expectation values of powers of the energy and 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 adding new moments, representing further expectation values of powers of energy, with respect to those already considered in Camiola and Romano (2014) does not improve the accuracy of the model.