H is definitely a state function as it is obtained by adding PV (P and V as state variables) to a state function U = U ( S , V , { N i } ) , so its differential is an exact differential. Because of d H = T d S + V d P + ∑ ∑ μ μ i d N i and the fact that it must be an exact differential, H = H ( S , P , { N i } ) .