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How to prove the Gibbs-Bogoliubov inequality

  1. May 10, 2009 #1
    Hi

    I need to prove the Gibbs-Bogoliubov inequality in two stages.
    First I need to prove that if I have a canonical partition function so:

    Q(N,V,T)>=Sigma(exp(-beta*<fi|H|fi>) by using the ritz variational principle
    fi = set of orthonormal functions in the hilbert space.
    Then... by using this inequality I need to prove that:
    A1=< A2+<H1-H2> which is the Gibbs-Bogoliubov inequality. (A is the free helmholtz energy, and H is hamiltonian)

    Anyone can help me or give me a link to a paper with the solution?

    Thanks

    Evan
     
  2. jcsd
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