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The Boltzmann factor is defined as

[itex]P_j=\frac{1}{Z}e^{-\beta E_j}[/itex]

I know, this is a probability distribution. but what exactly does it mean?

Wikipedia says: "The probability Pj that the system occupies microstate j" (link)

But that doesen make sense to me. cos [itex]\sum_i[/itex] is equal to 1.

That would only make sense if i look at ONLY 1 particle and not a system with n particles IMHO.

Then i got this Partition function Z.

It is defined as [itex]Z=\sum_i g_i e^{- \frac{E_i}{k_BT}[/itex]

with a factor gi denoting the degeneracy of energy states.

What is gi? i thought it's the number of different states in this energy level. but that's not likely cos in the Maxwell-Boltzmann distribution there's no pauli law...

thanks