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_{0}and let it evolve, it reachs equilibrium. Let U

_{eq}be the energy of the system at equilibrium.

Now take the same system with fixed energy U=U

_{eq}(S is not fixed anymore), how do you know that the equilibrium reached is the same as before, that means with entropy S

_{0}?

(I'm reading Callen's book on thermodynamics and he uses that fact in chapter 5 to prove the equivalence between the maximum entropy principle and the minimum energy principle.)