with Δ Δ θ θ j = ( θ θ − − θ θ 0 ) j a small change of θ θ in the j direction, and P j ( θ θ 0 ) = ∂ ∂ P ∂ ∂ θ θ j ( θ θ 0 ) the corresponding rate of change in the probability distribution. Since relative entropy has an absolute minimum 0 for P = Q , i.e. θ θ = θ θ 0 , it changes only to second order in the small parameters Δ Δ θ θ j . More formally, as for any minimum, the first derivatives of the divergence vanish