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Maximizing Gibbs Entropy in Canonical Ensemble

  1. Mar 14, 2012 #1
    Hey,

    Here is the problem:

    [​IMG]

    The method by which we solve is by Langrange Multipliers, and so I believe I found the derivative of f with respects to P(i) but I have two quantities I'm sure what they equal:

    Summations over i=1 to N : Ʃln(P(i)) and ƩE(i)

    Thanks for any help,
    S
     
  2. jcsd
  3. Mar 19, 2012 #2
    Remember you have N different quantities Pi that you are derivating with respect to. So for example if you have f(x,y) = x ln x + y ln y, then ∂f/∂x = ln x + 1 and likewise for y. There are no mixed terms, and even with a function of N variables, only one term survives the derivative.
     
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