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Helmholtz free energy in the canonical ensemble

  1. Apr 7, 2015 #1
    Hello everybody :D
    My question is: given the distribution of the canonical ensemble, how do we get the helmoltz free energy?
    I think we can't use A = U-TS because we don't know how to write S. So what's the solution? Thanks
     
  2. jcsd
  3. Apr 8, 2015 #2

    DrClaude

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    Staff: Mentor

    The simplest way is to use
    $$
    A = - k T \ln Z
    $$
     
  4. Apr 8, 2015 #3
    Thanks DrClaude, but I already know the result! How do you get that formula?
     
  5. Apr 8, 2015 #4

    DrClaude

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    Staff: Mentor

    You should be able to find the derivation in any statistical physics textbook. You can also find a derivation on Wikipedia.
     
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