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,&epsilon;1)/P(N2,&epsilon;2) = g(N0 - N1, U0 - &epsilon;1)/g(N0 - N2, U0 - &epsilon;2)

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

P(N1,&epsilon;1)/P(N2,&epsilon;2) = exp((N1&mu; - &epsilon;1)/T)/exp((N2&mu; - &epsilon;2)/T)

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