New extended thermodynamics balance equations for an electron gas confined in a metallic body

Sommerfeld’s theory of metal electrons suggests that the electrons in a metal can be described as a gas of free fermion particles confined inside the metallic body. In this paper a new extended thermodynamics model is proposed starting from this idea. The model includes both the stress tensor and a quadratic expansion of the distribution function in the neighborhhod of an equilibrium state. Such contributions were neglected in the original model proposed by Müller in 1976; so this new set of balance laws represents an improvement aimed at the description of non-equilibrium phenomena. The application to a simple case is briefly analysed.