Thermostatistics of classical fields

  • Sergey A. RashkovskiyEmail author
Regular Paper


In this paper, we consider 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.


Classical fields Phase space for classical field Thermostatistics Gibbs distribution Bose–Einstein distribution Fermi–Dirac distribution Gentile statistics Quantization 



This work was done on the theme of the State Task No. AAAA-A17-117021310385-6. Funding was provided in part by the Tomsk State University competitiveness improvement program.

Compliance with ethical standards

Conflict of interest

The author states that there is no conflict of interest.


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Copyright information

© Chapman University 2019

Authors and Affiliations

  1. 1.Ishlinsky Institute for Problems in Mechanics of the Russian Academy of SciencesMoscowRussia
  2. 2.Tomsk State UniversityTomskRussia

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