MB vs FD vs BE distributions — and the onset of Bose-Einstein condensation
Bose-Einstein condensation occurs below T_c = (ℏ²/2mk_B)(n/ζ(3/2))^(2/3). At T_c, μ→0 from below and the ground state acquires macroscopic occupation N₀/N = 1−(T/T_c)³. Fermi-Dirac statistics prohibit multiple occupancy (Pauli exclusion), while classical Maxwell-Boltzmann statistics ignore quantum exchange symmetry entirely.