# Jarzynski equality

The **Jarzynski equality**, also known as the *work relation* or *non-equilibrium work relation* was developed by Chris Jarzynski.
According to this equality, the equilibrium Helmholtz energy function of a process, (), can be reconstructed by averaging the external work, , performed in many non-equilibrium realizations of the process (Eq. 2a in ^{[1]}):

or can be trivially re-written as (Eq. 2b)

where is the Boltzmann constant and is the temperature. The only assumption in the proof of this relation is that of a weak coupling between the system and the reservoir. More recently Jarzynski has re-derived this formula, dispensing with this assumption ^{[2]}.

## See also[edit]

## References[edit]

**Related reading**

- Gerhard Hummer and Attila Szabo "Free energy reconstruction from nonequilibrium single-molecule pulling experiments", Proceedings of the National Academy of Sciences of the United States of America
**98**pp. 3658-3661 (2001) - E. G. D. Cohen and D. Mauzerall "The Jarzynski equality and the Boltzmann factor", Molecular Physics
**103**pp. 2923 - 2926 (2005) - L. Y. Chen "On the Crooks fluctuation theorem and the Jarzynski equality", Journal of Chemical Physics
**129**091101 (2008) - Eric N. Zimanyi and Robert J. Silbey "The work-Hamiltonian connection and the usefulness of the Jarzynski equality for free energy calculations", Journal of Chemical Physics
**130**171102 (2009) - Humberto Híjar and José M Ortiz de Zárate "Jarzynski's equality illustrated by simple examples", European Journal of Physics
**31**pp. 1097 (2010) - Christopher Jarzynski "Comparison of far-from-equilibrium work relations", Comptes Rendus Physique
**8**pp. 495-506 (2007)