The non-equilibrium temperature beyond local equilibrium assumption

In this manuscript, we propose a non-equilibrium temperature by a temperature dependent Vlasov equation for the charge particles transport through a environmental reservoir. A new damping force and a inverse damping relaxation time are derived based on the Vlasov equation, which have obvious influence on the external force and the relaxation time of transport particles. The non-equilibrium temperature for the transport particles is defined by their distribution function out of equilibrium, which is different from the equilibrium temperature of reservoir. There exists heat transfer between the transport particles and the reservoir, because the whole transport particles are in non-equilibrium state. Finally, we illustrate them by an example of one-dimensional charge particles transport under an external electric field, the non-equilibrium temperature and damping force defined by us are shown numerically.