Nonequilibrium approach regarding metals from a linearised kappa distribution

Abstract

The widely used kappa distribution functions develop high-energy tails through an adjustable kappa parameter. The aim of this work is to show that such a parameter can itself be regarded as a function, which entangles information about the sources of disequilibrium. We first derive and analyse an expanded Fermi–Dirac kappa distribution. Later, we use this expanded form to obtain an explicit analytical expression for the kappa parameter of a heated metal on which an external electric field is applied. We show that such a kappa index causes departures from equilibrium depending on the physical magnitudes. Finally, we study the role of temperature and electric field on such a parameter, which characterises the electron population of a metal out of equilibrium.