- At
*E=*0 (all particles in the ground state) both the system of bosons and the system of distinguishable particles have a degeneracy of 1. - For
*E=ε*, one excited particle, the boson system has*Ω=*1 and the distinguishable particle system has*Ω=N.* - For
*E=2ε*the boson system still has*Ω=*1. (That never changes, right?) The system of distinguishable particles has:

The Boltzmann factors decrease with increasing energy in exactly the same way for both distinguishable particles and bosons, but for distinguishable particles the growth in degeneracy overwhelms the decrease in that Boltzmann factor.