Statistical properties of a one-dimensional radiant cavity

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Abstract
The statistical properties of a classical electromagnetic field in interaction with matter are investigated. To this end a nonlinear extension of a model proposed elsewhere is studied by numerically solving the Newton-Maxwell equations of motion. The time-average energy distribution of the electromagnetic normal modes is also computed. It is shown that nonlinearity, no matter how large, does not completely destroy the dependence of the final energy distribution on initial conditions. One is therefore led to the conclusion that, as far as one is concerned with electrodynamical systems of finite total energy, no statistical behavior is to be expected. In particular, the Rayleigh-Jeans distribution law is not a general consequence of classical physics. The dependence on initial conditions can be removed, however, by the introduction of white noise delivering an infinite amount of energy to the radiation field. In this case equipartition of energy is reached, but in accordance with an old conjecture by Jeans, this process takes place at a nonuniform rate, the energy transfer being slower at higher frequencies.