Statistical Mechanics/Boltzmann and Gibbs factors and Partition functions/Gibbs Factors

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Using the same method as we did with Boltzmann Factors, we consider a system in thermal and diffusive equilibrium with another system.

P(N11)/P(N22) = g(N0 - N1, U0 - ε1)/g(N0 - N2, U0 - ε2)

And by the exact same method as our derivation of Boltzmann factors (no surprises here):

P(N11)/P(N22) = exp((N1μ - ε1)/T)/exp((N2μ - ε2)/T)

Which we will use in the exact same way to create the Grand Partition Function.