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| The '''Crooks fluctuation theorem''' was developed by Gavin E. Crooks. It is also known as the ''Crooks Identity'' or the ''Crooks fluctuation relation''. It is given by (<ref>[http://dx.doi.org/10.1103/PhysRevE.60.2721 Gavin E. Crooks "Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences", Physical Review E '''60''' pp. 2721-2726 (1999)]</ref> Eq. 2): | | The '''Crooks fluctuation theorem''' was developed by Gavin E. Crooks. It is also known as the ''Crooks Identity'' or the ''Crooks fluctuation relation''. |
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| | | :<math>\frac{P_F(W)}{P_R(-W)}= \exp \left( \frac{W-\Delta G}{k_BT} \right)</math> |
| :<math>\frac{P_F(+\omega)}{P_R(-\omega)}= \exp({+ \omega})</math> | |
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| where <math>\omega</math> is the [[entropy]] production, <math>P_F(\omega)</math> is the "forward" probability distribution of this entropy production, and <math>P_R(-\omega)</math>, time-reversed. This expression can be written in terms of [[work]] (<math>W</math>) (Eq. 11):
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| :<math>\frac{P_F(+\beta W)}{P_R(- \beta W)}= \exp (- \Delta A) \exp (+\beta W)</math>
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| where <math>\beta := 1/(k_BT)</math> where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]], and <math>A</math> is the [[Helmholtz energy function]].
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| ==See also==
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| *[[Jarzynski equality]]
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| ==References== | | ==References== |
| <references/>
| | #[http://dx.doi.org/10.1103/PhysRevE.60.2721 Gavin E. Crooks "Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences", Physical Review E '''60''' pp. 2721 - 2726 (1999)] |
| ;Related reading
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| *[http://dx.doi.org/10.1063/1.2978949 L. Y. Chen "On the Crooks fluctuation theorem and the Jarzynski equality", Journal of Chemical Physics '''129''' 091101 (2008)]
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| *[http://dx.doi.org/10.1063/1.3067878 Riccardo Chelli "Nonequilibrium work relations for systems subject to mechanical and thermal changes", Journal of Chemical Physics '''130''' 054102 (2009)]
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| [[category:Non-equilibrium thermodynamics]] | | [[category:Non-equilibrium thermodynamics]] |
| [[category: fluctuation theorem]] | | [[category: fluctuation theorem]] |