Five common thermodynamic potentials are:
where  = temperature,  = entropy,  = pressure,  = volume.  is the number of particles of type  in the system and  is the chemical potential for an -type particle. The set of all  are also included as natural variables but may be ignored when no chemical reactions are occurring which cause them to change. The Helmholtz free energy is in ISO/IEC standard called Helmholtz energy or Helmholtz function. It is often denoted by the symbol , but the use of  is preferred by IUPAC, ISO and IEC.
These five common potentials are all potential energies, but there are also entropy potentials. The thermodynamic square can be used as a tool to recall and derive some of the potentials.
Just as in mechanics, where potential energy is defined as capacity to do work, similarly different potentials have different meanings like the below:
* Internal energy () is the capacity to do work plus the capacity to release heat.
* Gibbs energy () is the capacity to do non-mechanical work.
* Enthalpy () is the capacity to do non-mechanical work plus the capacity to release heat.
* Helmholtz energy () is the capacity to do mechanical work plus non-mechanical work.
From these meanings (which actually apply in specific conditions, e.g. constant pressure, temperature, etc.), for positive changes (e.g., ), we can say that  is the energy added to the system,  is the total work done on it,  is the non-mechanical work done on it, and  is the sum of non-mechanical work done on the system and the heat given to it.
Note that the sum of internal energy is conserved, but the sum of Gibbs energy, or Helmholtz energy, are not conserved, despite being named "energy". They can be better interpreted as the potential to perform "useful work", and the potential can be wasted.
Thermodynamic potentials are very useful when calculating the equilibrium results of a chemical reaction, or when measuring the properties of materials in a chemical reaction. The chemical reactions usually take place under some constraints such as constant pressure and temperature, or constant entropy and volume, and when this is true, there is a corresponding thermodynamic potential that comes into play. Just as in mechanics, the system will tend towards a lower value of a potential and at equilibrium, under these constraints, the potential will take the unchanging minimum value. The thermodynamic potentials can also be used to estimate the total amount of energy available from a thermodynamic system under the appropriate constraint.
In particular: (see principle of minimum energy for a derivation)
* When the entropy  and "external parameters" (e.g. volume) of a closed system are held constant, the internal energy  decreases and reaches a minimum value at equilibrium. This follows from the first and second laws of thermodynamics and is called the principle of minimum energy. The following three statements are directly derivable from this principle.
* When the temperature  and external parameters of a closed system are held constant, the Helmholtz free energy  decreases and reaches a minimum value at equilibrium.
* When the pressure  and external parameters of a closed system are held constant, the enthalpy  decreases and reaches a minimum value at equilibrium.
* When the temperature , pressure  and external parameters of a closed system are held constant, the Gibbs free energy  decreases and reaches a minimum value at equilibrium.