On a generalized kinetic approach to Relativistic Extended Thermodynamics

Abstract

Extended Thermodynamics is applicable to many physical problems. Hydrodynamics models are also capable to describe the charge carrier transport in semi conductors, particularly with regard to hot electrons and submicron devices. In a recent paper [1] we considered the macroscopic model with an arbitrary but fixed number of moments for Relativistic E.T. and we found the closure consistent with the entropy principle and the Einstein relativity one, up to whatever order with respect to equilibrium. Everything was determined in terms of an arbitrary family of a single variable functions arising from integration. Subsequently, in paper [2], we proved that fixing a certain order np with respect to equilibrium and a scalar valued single variable function ψ, appearing at that order, then all the other terms appearing at orders n ≤ np are determined in terms of ψ, without introducing any other function. In this paper we will prove that the same result can be found also with a generalized kinetic approach. It has the advantage of being expressed in a more compact way. 1. M. Carrisi and S. Pennisi, An exact fluid model for relativistic electron beams: The many moments case, Journal of Math. Phys., vol. 48, no. 12, p. 123101, 2007. 2. M. Carrisi and S. Pennisi, A simplified exact macroscopic approach to relativistic extended thermodynamics, with an arbitrary number of moments, to be published.