 Natural variables of a thermodynamic potential

Natural variables are the independent variables appearing in the differential that directly identifies a potential's conjugate quantities. For $U(S,V,N)$, $dU=TdS-pdV+\mu dN$. Legendre transforms exchange a variable for its conjugate: $F=U-TS$ has natural variables $T,V,N$, and $G=F+pV$ has $T,p,N$. Equilibrium minimum principles require the corresponding environmental constraints and fixed conserved amounts.