What is the name of the thermodynamic potential F = U - TS?

The thermodynamic potential F = U − TS is the Helmholtz free energy. Here, U is internal energy, T is absolute temperature, and S is entropy. The symbol A is also widely used for the same quantity, especially in modern thermodynamics and chemistry.

Helmholtz free energy is especially useful for systems held at constant temperature and volume. Under those conditions, a decrease in Helmholtz energy indicates the maximum useful work that can be obtained in an idealized reversible process, apart from specified forms of non-expansion work. At equilibrium, the Helmholtz energy is minimized when temperature and volume are fixed.

The potential was named for German physicist Hermann von Helmholtz, who presented the idea in 1882 while discussing the thermodynamics of chemical processes. Its definition is a Legendre transformation of internal energy: entropy is replaced as an independent variable by temperature.

A common mix-up is Gibbs free energy, G = H − TS. Gibbs free energy is the more familiar choice for constant-temperature, constant-pressure chemistry, whereas Helmholtz free energy is natural for constant-temperature, constant-volume systems, such as idealized bomb-calorimeter measurements.