Maximizing Gibbs Entropy in Canonical Ensemble

Sekonda

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

clamtrox

Remember you have N different quantities P_i 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.