Gibbs Factor - need to have a sum that adds up all of the...

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Gibbs Factor We derived in Section 1 the Boltzmann factor by allowing the temperature to change. If we generalize and allow the number of particles to change as well, we can obtain a ratio of probabilities: = The structure of the above is very similar to what we encountered before. Ignoring the new term returns the familiar form from before. Any term of the form e (N μ - )/ τ is called a Gibbs factor. Gibbs Sum So far we only have a mechanism for relative probabilities. To obtain absolute probabilities, we
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Unformatted text preview: need to have a sum that adds up all of the Gibbs factors. This sum is called the Gibbs sum and is given by: Z G ( μ , τ ) = e (N μ-)/ τ Note that in taking the sum we begin with N = 0 , which has its own corresponding energies , and sum over all the states with N = 0 . Then we move to N = 1 , and so on. We can calculate the absolute probability of occupation of a state now using the Gibbs factor and the Gibbs sum just as we did with the Boltzmann factor and sum earlier....
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