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The motion of a charged pointlike relativistic particle under the action of a given force field plus a random electromagnetic radiation is studied. It is assumed that the given force field alone should produce a multiply periodic motion, which is perturbed by the action of both the random radiation and the reaction damping. The random radiation is represented by a stochastic process and an equation is obtained for the equilibrium probability density of the particle in phase space. In the particular case of a random radiation with Rayleigh-Jeans spectrum, it is shown that the stationary solution, corresponding to radiation-matter equilibrium, is given by the Maxwell-Boltzmann distribution

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Equilibrium between radiation and matter for classical relativistic multiperiodic systems. Derivation of Maxwell-Boltzmann distribution from Rayleigh-Jeans spectrum