In general, consider the extensive variable X and intensive variable Y where X and Y form a pair of conjugate variables. In ensembles where Y is fixed (and X is allowed to fluctuate), then the average value of X will be: ⟨ ⟨ X ⟩ ⟩ = ± ± ∂ ∂ ln ⁡ ⁡ Z ∂ ∂ β β Y .