The Temperature Dependent Boltzmann Equation with Reservoir of Radiation Photons

Abstract

Usually, the temperature is introduced by the Boltzmann distribution function under the local equilibrium assumption. In this manuscript, we propose a temperature dependent Boltzmann equation, where the temperature is taken into account by the collision of transport particles and the particles in the reservoir, and we assume the reservoir remain in an equilibrium or local equilibrium state with an external temperature. Different from the usual Boltzmann equation, our temperature dependent Boltzmann equation obtains a new damping force which originates from the collision between transport particle and reservoir and is contrary to the external force applied to the system, meanwhile the relaxation time is also affected by the derivative of the damping force. In our study, the reservoir are consist of the radiations of photons, so the Compton scattering happens between the transport particle and the photon. Finally, we illustrate them by the example of one-dimensional transport process, the damping force and the non-equilibrium temperature defined by us are shown.