For each thermodynamic potential, there are thermodynamic variables that need to be held constant to specify the potential value at a thermodynamical equilibrium state, such as independent variables for a mathematical function. These variables are termed the natural variables of that potential. The natural variables are important not only to specify the potential value at the equilibrium, but also because if a thermodynamic potential can be determined as a function of its natural variables, all of the thermodynamic properties of the system can be found by taking partial derivatives of that potential with respect to its natural variables and this is true for no other combination of variables. If a thermodynamic potential is not given as a function of its natural variables, it will not, in general, yield all of the thermodynamic properties of the system.
The set of natural variables for each of the above four thermodynamic potentials is formed from a combination of the , , ,  variables, excluding any pairs of conjugate variables; there is no natural variable set for a potential including the - or - variables together as conjugate variables for energy. An exception for this rule is the  −  conjugate pairs as there is no reason to ignore these in the thermodynamic potentials, and in fact we may additionally define the four potentials for each species. Using IUPAC notation in which the brackets contain the natural variables (other than the main four), we have:
If there is only one species, then we are done. But, if there are, say, two species, then there will be additional potentials such as  and so on. If there are  dimensions to the thermodynamic space, then there are  unique thermodynamic potentials. For the most simple case, a single phase ideal gas, there will be three dimensions, yielding eight thermodynamic potentials.