# Why at high energies, Fermi-Dirac and Bose-Einstein distribution behaves as Maxwell-Boltzman distribution? What is the physical explanantion?

I was searching for the reason that why at higher energies, the FD and BE distributions behave as MB distribution. In Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles by Eisberg and Resnick, 2nd edition, page 386 it is stated that:

At high energies ($$\epsilon>>kT$$) where the probable number of particles per quantum state for the classical distribution is much less than one, the quantum distributions merge with the classical distribution. That is $$n_{Fermi} \approx n_{Boltz} \approx n_{Bose}$$, if $$n_{Boltz}<<1$$.

My question is why in the first place, at higher energies, the number of particles in the MB distribution for per state will be less than $$1$$? As per my understanding, the three distributions should merge to the classical one only when one state could occupy more than one particle (violating the exclusion principle) and they become distinguishable. The math is alright, but I want to know the physics behind this phenomenon.

• Consider what happens when the probability of occupation of a given state is so low that two particles will never try to occupy it at the same time.. So they no longer care if they should be arguing (Fermi-Dirac) or not (Bose-Einstein) since it just doesn't matter. Nov 8 '21 at 19:55