 Jarzynski equality

Integrating the Crooks fluctuation theorem over work and using normalization of the reverse probability distribution givesConsequently Jensen's inequality gives $⟨W{⟩}_F\ge \Delta F$. Some realizations may nevertheless have $W<\Delta F$. This is a work relation with equilibrium endpoint preparations, while the integral fluctuation theorem for total entropy production uses the actual final forward distribution. ^[ref]

Jarzynski equality is a result in statistical mechanics that provides a relationship between the work done on a system during a non-equilibrium process and the change in free energy of the system. It was formulated by Christopher Jarzynski in 1997.