Title: The temperature dependent Boltzmann equation beyond local equilibrium assumption

Abstract: In this manuscript, we present a temperature dependent Boltzmann equation for the particles transport through a environmental reservoir, where the temperature refers to the equilibrium temperature of reservoir, a new damping force and a inverse damping relaxation time are derived based on the classical Boltzmann equation, which have obvious influence on the external force and the relaxation time of transport particles. For comparison, we also define a non-equilibrium temperature for the transport particle by its distribution function out of equilibrium, which is different from the equilibrium temperature of reservoir. There exist heat transfer between the transport particle and the reservoir, because the whole transport particles are in non-equilibrium state. Finally, we illustrate them by an example of one-dimensional transport procedure, the damping force and the non-equilibrium temperature defined by us are shown numerically.