# Maximizing Gibbs Entropy in Canonical Ensemble

by Sekonda
Tags: canonical, ensemble, entropy, gibbs, maximizing
 P: 209 Hey, Here is the problem: 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
P: 927
 Quote by Sekonda 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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