Thermostatistics of classical fields

Abstract

In this paper we develop the thermostatistics of the classical (continuous in space and time) fields. Assuming the thermodynamic equilibrium between the classical field and the thermal reservoir and the Gibbs statistics for the classical field, the probabilities of excitation of various modes of the classical field are determined. An artificial quantization of the classical field is considered, when the field energy is artificially divided into discrete portions - quanta with the same energy. The probability of excitation of a given number of quanta of a classical field is calculated. It is shown that if no restrictions are imposed on a classical field, then it obeys the Bose-Einstein statistics. If, however, an additional restriction is imposed on the amplitude of the classical field, it is described by a statistic analogous to the Fermi-Dirac statistics or the Gentile statistics, but does not coincide exactly with them.