Thermostatistics of classical fields

TL;DR

This paper develops the thermostatistics framework for classical fields, exploring their equilibrium properties, mode excitation probabilities, and how restrictions on the field influence their statistical behavior, including Bose-Einstein and Fermi-Dirac analogs.

Contribution

It introduces a novel approach to classical field thermostatistics, including artificial quantization and the impact of amplitude restrictions on statistical behavior.

Findings

Classical fields obey Bose-Einstein statistics without restrictions.

Restrictions on amplitude lead to statistics similar to Fermi-Dirac or Gentile.

Probabilities of mode excitation are explicitly calculated.

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.