“…The motivation for studying a two-temperature electron plasma is due to fact that although there is no direct observational evidence for the existence of two groups of electrons in relativistic degenerate regimes, based on the information available from the theories and some relevant observations, it is expected that such highly relativistic degenerate astrophysical plasmas coexisting with classical relativistic hot electron flow can exist, e.g., during the formation of relativistic jets due to accretion-induced collapsing of white dwarfs into black holes (Begelman et al, 1984;Kryvdyk, 1999;Kryvdyk and Agapitov, 2007). The relativistic dense plasmas where the background distribution of electrons deviates from the thermodynamic equilibrium can also appear in the context of laser produced plasmas or ion beam driven plasmas (Gibbon, 2005;Hau-Riege, 2011). In such cases, the system energy mostly flows into the electrons, thereby generating fully degenerate electrons with long tails or partially degenerate electrons with high temperature tails, and allowing the division of background electrons with two different temperatures.…”