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The nonextensive Bose-Einstein condensation and photon gas with parameter transformation

  • Pengfei Ma
  • Yahui ZhengEmail author
  • Guangyue Qi
Regular Article

Abstract.

The nonextensive boson system is revisited with the statistical ensemble theory, where the fundamental grand canonical distribution is derived from the equiprobability principle. By recourse to the approach of parameter transformation, one familiar and concise statistical formula for bosons is deduced, in an accurate fashion. Then the Bose-Einstein condensation phenomenon is re-discussed. The results show that the critical temperature is dependent on the nonextensive parameter \( \nu\) , and in the generalized expression of the heat capacity for the condensated phase of boson systems there exists one additional term, obeying the T3 law. By use of the statistical formula, the nonextensive photon gas is also researched. The internal energy and heat capacity for the nonextensive photon gas exhibit a similar dependence on the temperature to the classical photon gas, apart from a coefficient correction dependent on the parameter \( \nu\) . The Gibbs function for the nonextensive photon gas is still zero, showing that the photon field is also at thermal equilibrium, like the situation of classical photon field. The entropy of photon field can be calculated through the integral of the nonextensive quantum statistics formula and can also be derived from the original definition of Tsallis entropy, by recourse to the direct parameter transformation. This seems to indicate the validity of the treatment technique for the nonextensive quantum systems.

Notes

Author contribution statement

Two of the authors, PM and YZ, contributed equally to this work.

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Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of 3D PrintingXinxiang UniversityXinxiang CityChina
  2. 2.School of ScienceHenan Institute of TechnologyXinxiang CityChina
  3. 3.LibraryHenan Institute of TechnologyXinxiang CityChina

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