Thermodynamic potential

In thermodynamics, thermodynamic potentials are parameters associated with a thermodynamic system and have the dimensions of energy. They are called "potentials" because in a sense, they describe the amount of potential energy in a thermodynamic system when it is subjected to certain constraints. The different potentials correspond to different constraints to which the system may be subjected. The four most common thermodynamic potentials are:

Name	Formula	Natural variables
Internal energy	${\displaystyle U\,}$	${\displaystyle ~~~~~S,V,\{N_{i}\}\,}$
Helmholtz free energy	${\displaystyle A=U-TS\,}$	${\displaystyle ~~~~~T,V,\{N_{i}\}\,}$
Enthalpy	${\displaystyle H=U+pV\,}$	${\displaystyle ~~~~~S,p,\{N_{i}\}\,}$
Gibbs free energy	${\displaystyle G=U+pV-TS\,}$	${\displaystyle ~~~~~T,p,\{N_{i}\}\,}$

where T = temperature, S = entropy, p = pressure, V = volume. The Helmholtz free energy is often denoted by the symbol F, but the use of A is preferred by IUPAC (See Alberty, 2001). ${\displaystyle N_{i}}$ is the number of particles of type i in the system. For the sake of completeness, the set of all ${\displaystyle N_{i}}$ are also included as natural variables, although they are sometimes ignored.