How to prove the Gibbs-Bogoliubov inequality

1. May 10, 2009

evantop

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