The Non-Equilibrium Temperature Beyond Local Equilibrium Assumption

We propose a non-equilibrium temperature for the particles transporting through its surroundings, which is expressed by the distribution function of a temperature dependent Vlasov equation, where we haven't adopted the local equilibrium hypothesis but introduced a equilibrium temperature by the surroundings. A temperature dependent damping force and a inverse damping relaxation time are obtained based on the Vlasov equation, which can be regarded as corrections on the external force and the relaxation time of transport procedure. The relation between the non-equilibrium temperature of transport particles and the equilibrium temperature of surroundings is established, too. There exist heat transfer between the transport particles out of equilibrium and the surroundings in equilibrium. Finally, we illustrate them by a system of one-dimensional charge transport.