R. Alvarez, J. Cotrino, A. Palmero
EPL (Europhysics Letters), 105 (2014) 1
doi: 10.1209/0295-5075/105/15001

The framework to describe the out-of-equilibrium free electrons in cold plasmas is developed assuming the electron entropy is defined through the Boltzmann H-theorem. Our theory explains why the Saha-Boltzmann relation among higher-lying excited states by means of the electron kinetic temperature is fulfilled, even when free electrons are far from equilibrium. The thermodynamic electron temperature, pressure and chemical potential have been introduced through the derivatives of the electron entropy. It is demonstrated that under usual conditions in cold plasmas, e.g. when the electron distribution function possesses the Maxwellian, Druyvestein or Kappa functional forms, kinetic and thermodynamic electron temperatures yield the same value.