Maximizing Gibbs Entropy in Canonical Ensemble

  • Thread starter Sekonda
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  • #1
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Hey,

Here is the problem:

vGVcq.jpg


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
 

Answers and Replies

  • #2
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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

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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