The phrase "free energy" has multiple definitions in science:

### Thermodynamic Free Energy

In physics and physical chemistry, free energy refers to the amount of internal energy of a thermodynamic system that is available to perform work. There are different forms of thermodynamic free energy:

**Gibbs free energy** is the energy that may be converted into work in a system that is at constant temperature and pressure.

The equation for Gibbs free energy is:

G = H – TS

where G is Gibbs free energy, H is enthalpy, T is temperature, and S is entropy.

**Helmholtz free energy** is energy that may be converted into work at constant temperature and volume.

The equation for Helmholtz free energy is:

A = U – TS

where A is the Helmholtz free energy, U is the internal energy of the system, T is the absolute temperature (Kelvin) and S is the entropy of the system.

**Landau free energy** describes energy of an open system in which particles and energy may be exchanged with the surroundings.

The equation for Landau free energy is:

Ω = A - μN = U - TS - μN

where N is the number of particles and μ is chemical potential.

### Variational Free Energy

In information theory, variational free energy is a construct used in variational Bayesian methods. Such methods are used to approximate intractable integrals for statistics and machine learning.

### Other Definitions

In environmental science and economics, the phrase "free energy" is sometimes used to refer to renewable resources or any energy that does not require monetary payment.

Free energy may also refer to the energy that powers a hypothetical perpetual motion machine. Such a device violates the laws of thermodynamics, so this definition currently refers to a pseudoscience rather than hard science.

### Sources

- Baierlein, Ralph.
*Thermal Physics*. Cambridge University Press, 2003, Cambridge, U.K. - Mendoza, E.; Clapeyron, E.; Carnot, R., eds.
*Reflections on the Motive Power of Fire – and other Papers on the Second Law of Thermodynamics*. Dover Publications, 1988, Mineola, N.Y. - Stoner, Clinton. “Inquiries into the Nature of Free Energy and Entropy in Respect to Biochemical Thermodynamics.”
*Entropy*, vol. 2, no. 3, Sept. 2000, pp. 106–141., doi:10.3390/e2030106.