0
$\begingroup$

Both Fermi-Dirac and Bose-Einstein statistics reduce to the Maxwell-Boltzmann statistics in the classical limit of very high temperatures or very low concentration. In the case of very high temperatures, I suppose that the particles should be distributed uniformly among it's accessible states, so is Maxwell-Boltzmann distribution a uniform distribution?

$\endgroup$
  • $\begingroup$ I'm supposing you don't mean "uniform" in the sense of $P(x,a,b)=1/(b-a)$ sense of the PDF? $\endgroup$ – Kyle Kanos Apr 30 '19 at 15:34
  • $\begingroup$ That was my confusion at start: uniform in the sense of having equal number of particles in each state. $\endgroup$ – RicardoP Apr 30 '19 at 15:46
2
$\begingroup$

The Maxwell-Boltzmann distribution at high temperatures is a uniform distribution. Each energy level with energy $E_i$ comes with a weight (neglecting normalization) $e^{-E_i/k_B T}$. If $T$ is very large, we can expand this in orders of $1/T$. The leading term, as with any exponential, is just $1$. Of course, you can do this expansion for any temperature, but it only makes sense to focus on the first term at large $T$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.