Jarzynski equality

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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, (A), can be reconstructed by averaging the external work, W, performed in many non-equilibrium realizations of the process (Eq. 2a in [1]):

\exp \left( \frac{-\Delta A}{k_BT}\right)= \left\langle \exp \left( \frac{-W}{k_BT} \right) \right\rangle

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

\Delta A = - k_BT \ln \left\langle \exp \left( \frac{-W}{k_BT} \right) \right\rangle

where k_B is the Boltzmann constant and T 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].

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