We can use the above equations to derive some differential definitions of some thermodynamic parameters. If we define  to stand for any of the thermodynamic potentials, then the above equations are of the form:
where  and  are conjugate pairs, and the  are the natural variables of the potential . From the chain rule it follows that:
where  is the set of all natural variables of  except  that are held as constants. This yields expressions for various thermodynamic parameters in terms of the derivatives of the potentials with respect to their natural variables. These equations are known as equations of state since they specify parameters of the thermodynamic state. If we restrict ourselves to the potentials  (Internal energy),  (Helmholtz energy),  (Enthalpy) and  (Gibbs energy), then we have the following equations of state (subscripts showing natural variables that are held as constants):
where, in the last equation,  is any of the thermodynamic potentials (, , , or ), and  are the set of natural variables for that potential, excluding . If we use all thermodynamic potentials, then we will have more equations of state such as
and so on. In all, if the thermodynamic space is  dimensions, then there will be  equations for each potential, resulting in a total of  equations of state because  thermodynamic potentials exist. If the  equations of state for a particular potential are known, then the fundamental equation for that potential (i.e., the exact differential of the thermodynamic potential) can be determined. This means that all thermodynamic information about the system will be known because the fundamental equations for any other potential can be found via the Legendre transforms and the corresponding equations of state for each potential as partial derivatives of the potential can also be found.