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The '''Jarzynski equality''' | The '''Jarzynski equality''' is also known as the ''work relation'' or ''non-equilibrium work relation''. | ||
According to this equality, the equilibrium [[Helmholtz energy function]] of a process, (<math>A</math>), can be reconstructed by averaging the external [[work]], <math>W</math>, performed in many [[Non-equilibrium thermodynamics | non-equilibrium]] realizations of the process (Eq. 2a in <ref>[http://dx.doi.org/10.1103/PhysRevLett.78.2690 | According to this equality, the equilibrium [[Helmholtz energy function]] of a process, (<math>A</math>), can be reconstructed by averaging the external [[work]], <math>W</math>, performed in many [[Non-equilibrium thermodynamics | non-equilibrium]] realizations of the process (Eq. 2a in <ref>[http://dx.doi.org/10.1103/PhysRevLett.78.2690 C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters '''78''' 2690-2693 (1997)]</ref>): | ||
:<math>\exp \left( \frac{-\Delta A}{k_BT}\right)= \left\langle \exp \left( \frac{-W}{k_BT} \right) \right\rangle</math> | :<math>\exp \left( \frac{-\Delta A}{k_BT}\right)= \left\langle \exp \left( \frac{-W}{k_BT} \right) \right\rangle</math> | ||
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:<math>\Delta A = - k_BT \ln \left\langle \exp \left( \frac{-W}{k_BT} \right) \right\rangle </math> | :<math>\Delta A = - k_BT \ln \left\langle \exp \left( \frac{-W}{k_BT} \right) \right\rangle </math> | ||
where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]]. The only assumption in the proof of this relation is that of a weak coupling between the system and the reservoir | where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]]. The only assumption in the proof of this relation is that of a weak coupling between the system and the reservoir. | ||
==See also== | ==See also== | ||
*[[Crooks fluctuation theorem]] | *[[Crooks fluctuation theorem]] |