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

Using the same method as we did with Boltzmann Factors, we consider a system in thermal and diffusive equilibrium with another system. P(N1,ε1)/P(N2,ε2) = 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(N1,ε1)/P(N2,ε2) = exp((N1μ - ε1)/T)/exp((N2μ - ε2)/T) Which we will use in the exact same way to create the Grand Partition Function.