Is Degeneracy in Quantum States Equally Probable in Thermodynamic Equilibrium?

[hokhani]

In Wikipedia this sentence is written about degeneracy;
In physics, two or more different quantum states are said to be degenerate if they are all at the same energy level. Statistically this means that they are all equally probable of being filled,
do you agree with the bold statement?

 

[Einj]

I think this could be correct since the Boltzmann distribution is given by:

$$p(E_i)=\frac{1}{Z}\exp^{-E_i/kT}$$

so the probability density of finding a particle in two state with the same energy should be the same.

 

[Bill_K]

If they are mutually accessible, and the system is in thermodynamic equilibrium. This is the "Postulate of Equal a Priori Probability."

 

[Amok]

To me this makes complete sense if you consider that the system is in thermodynamic equilibrium. Think of how it is less likely that particles occupy higher energy levels than lower ones. In