Jarzynski equality

The Jarzynski equality is also known as the work relation or non-equilibrium work relation. According to this equality, the equilibrium free energy of a process, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta G} , can be reconstructed by averaging the external work, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W} , performed in many nonequilibrium realizations of the process:

$\exp \left({\frac {-\Delta G}{k_{B}T}}\right)=\left\langle \exp \left({\frac {-W}{k_{B}T}}\right)\right\rangle$

References

1. C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters 78 2690-2693 (1997)
2. E. G. D. Cohen; D. Mauzerall "The Jarzynski equality and the Boltzmann factor", Molecular Physics 103 pp. 2923 - 2926 (2005)