The purpose of this paper is firstly the general analysis of systems whose internal energy depends upon more state functions. Then, some particular systems are analyzed in detail. Magnetic systems depending on three or two independent state functions are considered and reference is made in particular to ferrofluids.

Dielectric systems depending on three or two independent state functions are examined and reference is made in particular to condensers used to convert solar into electrical energy. Chemically reacting systems with three independent state functions are examined. The thermodynamic relations for the usual fluids depending upon two state functions are obtained as a particular case in the absence of chemical state function. Systems with surface tension and one-dimensional elastic systems are dealt with.

In addition, a system depending on four independent state functions is synthetically examined.