Abstract
The relaxation back to thermal equilibrium of one very dilute species of charged particle in a heat bath of different neutral particles, with which they collide elastically, is considered by means of the Boltzmann equation for the one-particle distribution function of the test particles. The Boltzmann collision integral is used to describe the collisions. A rigorous proof that relaxation to thermal equilibrium will always take place, even in the presence of a magnetic field, is given, initially for the case when there is no spatial dependence. The proof is based on a functional of the distribution function with properties similar to the Boltzmann entropy. This quantity is shown always to decrease until thermal equilibrium is reached, and to be bounded below by its value in thermal equilibrium. The proof is then generalised to allow for arbitrary spatial dependence of the magnetic field and the initial distribution function.
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