How does the Boltzmann statistic relate to systems at high temperatures?

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The discussion centers on the validity of the Boltzmann statistic in high-temperature systems, referencing the Maxwell-Boltzmann statistics. It emphasizes that most systems at elevated temperatures conform to classical limits unless they exhibit high density, as seen in white dwarfs. The conversation highlights that both Fermi-Dirac and Bose-Einstein statistics approximate Maxwell-Boltzmann under high temperature or low concentration conditions. There is also a mention of the need for clarity on what "correct" means, suggesting "approximately correct" might be more appropriate. The importance of understanding the limits of applicability in these statistical mechanics contexts is underscored.
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Because the two derivations provided at your reference work!

"...most systems at high temperatures obey the classical (Maxwell–Boltzmann) limit unless they have a very high density, as for a white dwarf. Both Fermi–Dirac and Bose–Einstein become Maxwell–Boltzmann statistics at high temperature or at low concentration..."


It also depends on what your mean by "correct"..."approximately correct" would perhaps be a better description... did you see the "limits of applicability"...??
 
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