The internal energy of a system depends on its entropy S, its volume V and its number of massive particles: U (S, V,{ N j }). It expresses the thermodynamics of a system in the energy representation. As a function of state, its arguments are exclusively extensive variables of state. Alongside the internal energy, the other cardinal function of state of a thermodynamic system is its entropy, as a function, S (U, V,{ N j }), of the same list of extensive variables of state, except that the entropy, S, is replaced in the list by the internal energy, U. It expresses the entropy representation.