*This article discusses the thermodynamics term of "free energy", see Free energy (disambiguation) for other possible uses.*

In thermodynamics, the term ** free energy** denotes either of two related concepts of importance. They express the total amount of energy which is used up or released during a chemical reaction. Both attempt to capture that part of the total energy of a system which is available for "useful work" and is hence not stored in "useless random thermal motion". As a system undergoes changes, its free energy will decrease.

When a system of molecules undergoes change, whether chemical reaction or changes in physical states such as phase changes, there are two tendencies driving the changes:

If**E**represents the energy,

**T**the temperature, and

**S**the entropy, these two tendencies can be combined by stating that the expression

- E - TS, the Helmholtz function

**P**represents the pressure and

**V**represents the volume) replaces the energy, and thus the quantity that must be minimized is

- H - TS = E + PV - TS, the Gibbs function.

*free energy*and the symbol

**F**for the Helmholtz function, using

**G**to represent the Gibbs function; chemists have preferred to denote the Helmholtz function by

**A**[from the German word

*Arbeit*(=work)] and call it the

*work content*, reserving the term

*free energy*and the symbol

**F**for the Gibbs function. Recently a compromise notation has become common, using

**A**for the Helmholtz function,

**G**for the Gibbs function, and avoiding

**F**entirely. The functions are then referred to as the

*Helmholtz free energy*and

*Gibbs free energy.*