This exact result can be obtained from the general BAR method, using (for example) the Metropolis function, in the limit C → → − − ∞ ∞ . Indeed, in that case, the denominator of the general case expression above tends to 1, while the numerator tends to e β β C ⟨ e − − β β ( U B − − U A ) ⟩ A . A direct derivation from the definitions is more straightforward, though.