Crooks fluctuation theorem - Revision history

Carl McBride: Added an internal link

2011-07-05T09:31:48Z

Added an internal link

← Older revision		Revision as of 11:31, 5 July 2011
Line 1:		Line 1:
	~~{{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>[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''. It is given by (~~Ref~~. 1 Eq. 2):


Line 6:		Line 5:


	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):		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):


Line 13:		Line 12:

	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]].		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)]		<references/>
	#[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)]		;Related reading
	#[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/10.1063/1.2978949 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:Non-equilibrium thermodynamics]]
	[[category: fluctuation theorem]]		[[category: fluctuation theorem]]

Nice and Tidy: /* References */ Added a new reference.

2009-02-08T14:58:15Z

References: Added a new reference.

← Older revision		Revision as of 16:58, 8 February 2009
Line 16:		Line 16:
	#[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/10.1103/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/10.1063/1.2978949 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:Non-equilibrium thermodynamics]]
	[[category: fluctuation theorem]]		[[category: fluctuation theorem]]

Carl McBride: /* References */ Added a reference

2008-09-05T13:56:37Z

References: Added a reference

← Older revision		Revision as of 15:56, 5 September 2008
Line 15:		Line 15:
	==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)]		#[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)]
	[[category:Non-equilibrium thermodynamics]]		[[category:Non-equilibrium thermodynamics]]
	[[category: fluctuation theorem]]		[[category: fluctuation theorem]]

Carl McBride at 10:53, 6 February 2008

2008-02-06T10:53:14Z

← Older revision		Revision as of 12:53, 6 February 2008
Line 1:		Line 1:
	{{Stub-general}}		{{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''.		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(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>


			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==		==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/10.1103/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)]
	[[category:Non-equilibrium thermodynamics]]		[[category:Non-equilibrium thermodynamics]]
	[[category: fluctuation theorem]]		[[category: fluctuation theorem]]

Nice and Tidy at 10:30, 27 September 2007

2007-09-27T10:30:55Z

← Older revision		Revision as of 12:30, 27 September 2007
Line 1:		Line 1:
			{{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''.		The '''Crooks fluctuation theorem''' was developed by Gavin E. Crooks. It is also known as the ''Crooks Identity'' or the ''Crooks fluctuation relation''.

Carl McBride at 12:56, 13 June 2007

2007-06-13T12:56:13Z

← Older revision		Revision as of 14:56, 13 June 2007
Line 2:		Line 2:

	:<math>\frac{P_F(W)}{P_R(-W)}= \exp \left( \frac{W-\Delta G}{k_BT} \right)</math>		:<math>\frac{P_F(W)}{P_R(-W)}= \exp \left( \frac{W-\Delta G}{k_BT} \right)</math>
	~~==See also==~~
	*[[Jarzynski equality]]
	*[[Gallavotti-Cohen fluctuation theorem]]
	==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)]		#[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)]
	[[category:Non-equilibrium thermodynamics]]		[[category:Non-equilibrium thermodynamics]]
			[[category: fluctuation theorem]]

Carl McBride at 12:55, 13 June 2007

2007-06-13T12:55:22Z

← Older revision		Revision as of 14:55, 13 June 2007
Line 1:		Line 1:
	The '''Crooks fluctuation theorem''' was developed by Gavin E. Crooks.		The '''Crooks fluctuation theorem''' was developed by Gavin E. Crooks. It is also known as the ''Crooks Identity'' or the ''Crooks fluctuation relation''.

	:<math>\frac{P_F(W)}{P_R(-W)}= \exp \left( \frac{W-\Delta G}{k_BT} \right)</math>		:<math>\frac{P_F(W)}{P_R(-W)}= \exp \left( \frac{W-\Delta G}{k_BT} \right)</math>

Carl McBride at 13:44, 28 May 2007

2007-05-28T13:44:16Z

← Older revision		Revision as of 15:44, 28 May 2007
Line 1:		Line 1:
	:<math>\frac{P_F(W)}{P_R(-W)}= \exp \frac{W-\Delta G}{k_BT}</math>		The '''Crooks fluctuation theorem''' was developed by Gavin E. Crooks.

			:<math>\frac{P_F(W)}{P_R(-W)}= \exp \left( \frac{W-\Delta G}{k_BT} \right)</math>
			==See also==
			*[[Jarzynski equality]]
			*[[Gallavotti-Cohen fluctuation theorem]]
			==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)]
			[[category:Non-equilibrium thermodynamics]]

Carl McBride: New page: : $\frac{P_F(W)}{P_R(-W)}= \exp \frac{W-\Delta G}{k_BT}$

2007-05-28T13:39:58Z

New page: :<math>\frac{P_F(W)}{P_R(-W)}= \exp \frac{W-\Delta G}{k_BT}</math>

New page

:<math>\frac{P_F(W)}{P_R(-W)}= \exp \frac{W-\Delta G}{k_BT}</math>