Editing Crooks fluctuation theorem

{{Stub-general}}
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. 1 Eq. 2):


:<math>\frac{P_F(+\omega)}{P_R(-\omega)}= \exp({+ \omega})</math>


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>) (Ref. 1 Eq. 11):


:<math>\frac{P_F(+\beta W)}{P_R(- \beta W)}= \exp (- \Delta A) \exp (+\beta W)</math>


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]].
==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)]
#[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)]
#[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)]
[[category:Non-equilibrium thermodynamics]]
[[category: fluctuation theorem]]
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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):
+{{Stub-general}}
+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. 1 Eq. 2):
@@ Line 5: / Line 6: @@
-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):
+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>) (Ref. 1 Eq. 11):
@@ Line 12: / Line 13: @@
 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]].
-==See also==
-*[[Jarzynski equality]]
 ==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
+#[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)]
-*[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)]
+#[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)]
-*[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)]
 [[category:Non-equilibrium thermodynamics]]
 [[category: fluctuation theorem]]