Jarzynski equality - Revision history

Carl McBride: /* References */ Added a publication

2011-07-05T09:52:14Z

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	*[http://dx.doi.org/10.1063/1.3132747 Eric N. Zimanyi and Robert J. Silbey "The work-Hamiltonian connection and the usefulness of the Jarzynski equality for free energy calculations", Journal of Chemical Physics '''130''' 171102 (2009)]		*[http://dx.doi.org/10.1063/1.3132747 Eric N. Zimanyi and Robert J. Silbey "The work-Hamiltonian connection and the usefulness of the Jarzynski equality for free energy calculations", Journal of Chemical Physics '''130''' 171102 (2009)]
	*[http://dx.doi.org/10.1088/0143-0807/31/5/012 Humberto Híjar and José M Ortiz de Zárate "Jarzynski's equality illustrated by simple examples", European Journal of Physics '''31''' pp. 1097 (2010)]		*[http://dx.doi.org/10.1088/0143-0807/31/5/012 Humberto Híjar and José M Ortiz de Zárate "Jarzynski's equality illustrated by simple examples", European Journal of Physics '''31''' pp. 1097 (2010)]
			*[http://dx.doi.org/10.1016/j.crhy.2007.04.010 Christopher Jarzynski "Comparison of far-from-equilibrium work relations", Comptes Rendus Physique '''8''' pp. 495-506 (2007)]


	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]
	[[category: fluctuation theorem]]		[[category: fluctuation theorem]]

Carl McBride: Added a reference

2011-07-05T09:41:25Z

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← Older revision		Revision as of 11:41, 5 July 2011
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	The '''Jarzynski equality''' is also known as the ''work relation'' or ''non-equilibrium work relation''.		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, (<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>):		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 Chris 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. More recently Jarzynski has re-derived this formula, dispensing with this assumption <ref>[http://dx.doi.org/10.1088/1742-5468/2004/09/P09005 Chris Jarzynski "Nonequilibrium work theorem for a system strongly coupled to a thermal environment", Journal of Statistical Mechanics: Theory and Experiment P09005 (2004)]</ref>.
	==See also==		==See also==
	*[[Crooks fluctuation theorem]]		*[[Crooks fluctuation theorem]]

Carl McBride: Added an internal link

2011-07-05T09:29:49Z

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← Older revision		Revision as of 11:29, 5 July 2011
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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==
			*[[Crooks fluctuation theorem]]
	==References==		==References==
	<references/>		<references/>

Carl McBride: Slight tidy + Cite

2011-06-15T12:44:11Z

Slight tidy + Cite

← Older revision		Revision as of 14:44, 15 June 2011
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	The '''Jarzynski equality''' is also known as the ''work relation'' or ''non-equilibrium work relation''.		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>~~\Delta~~ A</math>, can be reconstructed by averaging the external [[work]], <math>W</math>, performed in many ~~nonequilibrium~~ realizations of the process (~~Ref. 1~~ Eq. 2a):		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>

	or can be trivially re-written as (~~Ref. 1~~ Eq. 2b)		or can be trivially re-written as (Eq. 2b)

	:<math>\Delta A = - ~~\frac{1}{~~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 proof of this ~~equation is given in Ref. 1 and the only assumption~~ 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.
	==References==		==References==
	~~#[http:~~/~~/dx.doi.org/10.1103/PhysRevLett.78.2690 C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters '''78''' 2690-2693 (1997)]~~		<references/>
	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1073/pnas.071034098 Gerhard Hummer and Attila Szabo "Free energy reconstruction from nonequilibrium single-molecule pulling experiments", Proceedings of the National Academy of Sciences of the United States of America '''98''' pp. 3658-3661 (2001)]		*[http://dx.doi.org/10.1073/pnas.071034098 Gerhard Hummer and Attila Szabo "Free energy reconstruction from nonequilibrium single-molecule pulling experiments", Proceedings of the National Academy of Sciences of the United States of America '''98''' pp. 3658-3661 (2001)]

Carl McBride: /* References */ Added a publication

2011-06-10T13:43:00Z

References: Added a publication

← Older revision		Revision as of 15:43, 10 June 2011
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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)]		*[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/10.1063/1.3132747 Eric N. Zimanyi and Robert J. Silbey "The work-Hamiltonian connection and the usefulness of the Jarzynski equality for free energy calculations", Journal of Chemical Physics '''130''' 171102 (2009)]		*[http://dx.doi.org/10.1063/1.3132747 Eric N. Zimanyi and Robert J. Silbey "The work-Hamiltonian connection and the usefulness of the Jarzynski equality for free energy calculations", Journal of Chemical Physics '''130''' 171102 (2009)]
			*[http://dx.doi.org/10.1088/0143-0807/31/5/012 Humberto Híjar and José M Ortiz de Zárate "Jarzynski's equality illustrated by simple examples", European Journal of Physics '''31''' pp. 1097 (2010)]

	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]
	[[category: fluctuation theorem]]		[[category: fluctuation theorem]]

Carl McBride: /* References */ Added a publication

2010-03-11T17:38:36Z

References: Added a publication

← Older revision		Revision as of 19:38, 11 March 2010
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	#[http://dx.doi.org/10.1103/PhysRevLett.78.2690 C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters '''78''' 2690-2693 (1997)]		#[http://dx.doi.org/10.1103/PhysRevLett.78.2690 C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters '''78''' 2690-2693 (1997)]
	'''Related reading'''		'''Related reading'''
	*[http://dx.doi.org/10.1080/00268970500151536 E. G. D. Cohen; D. Mauzerall "The Jarzynski equality and the Boltzmann factor", Molecular Physics '''103''' pp. 2923 - 2926 (2005)]		*[http://dx.doi.org/10.1073/pnas.071034098 Gerhard Hummer and Attila Szabo "Free energy reconstruction from nonequilibrium single-molecule pulling experiments", Proceedings of the National Academy of Sciences of the United States of America '''98''' pp. 3658-3661 (2001)]
			*[http://dx.doi.org/10.1080/00268970500151536 E. G. D. Cohen and D. Mauzerall "The Jarzynski equality and the Boltzmann factor", Molecular Physics '''103''' pp. 2923 - 2926 (2005)]
	*[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/10.1063/1.3132747 Eric N. Zimanyi and Robert J. Silbey "The work-Hamiltonian connection and the usefulness of the Jarzynski equality for free energy calculations", Journal of Chemical Physics '''130''' 171102 (2009)]		*[http://dx.doi.org/10.1063/1.3132747 Eric N. Zimanyi and Robert J. Silbey "The work-Hamiltonian connection and the usefulness of the Jarzynski equality for free energy calculations", Journal of Chemical Physics '''130''' 171102 (2009)]

Carl McBride: Added a publication

2010-03-11T17:29:19Z

Added a publication

← Older revision		Revision as of 19:29, 11 March 2010
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	~~{{Stub-general}}~~
	The '''Jarzynski equality''' is also known as the ''work relation'' or ''non-equilibrium work relation''.		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>\Delta A</math>, can be reconstructed by averaging the external [[work]], <math>W</math>, performed in many nonequilibrium realizations of the process (Ref. 1 Eq. 2a):		According to this equality, the ''equilibrium'' [[Helmholtz energy function]] of a process, <math>\Delta A</math>, can be reconstructed by averaging the external [[work]], <math>W</math>, performed in many nonequilibrium realizations of the process (Ref. 1 Eq. 2a):
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	==References==		==References==
	#[http://dx.doi.org/10.1103/PhysRevLett.78.2690 C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters '''78''' 2690-2693 (1997)]		#[http://dx.doi.org/10.1103/PhysRevLett.78.2690 C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters '''78''' 2690-2693 (1997)]
	#[http://dx.doi.org/10.1080/00268970500151536 E. G. D. Cohen; D. Mauzerall "The Jarzynski equality and the Boltzmann factor", Molecular Physics '''103''' pp. 2923 - 2926 (2005)]		'''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/10.1080/00268970500151536 E. G. D. Cohen; D. Mauzerall "The Jarzynski equality and the Boltzmann factor", Molecular Physics '''103''' pp. 2923 - 2926 (2005)]
			*[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/10.1063/1.3132747 Eric N. Zimanyi and Robert J. Silbey "The work-Hamiltonian connection and the usefulness of the Jarzynski equality for free energy calculations", Journal of Chemical Physics '''130''' 171102 (2009)]

	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]
	[[category: fluctuation theorem]]		[[category: fluctuation theorem]]

Carl McBride: /* References */ Added a reference

2008-09-05T13:57:12Z

References: Added a reference

← Older revision		Revision as of 15:57, 5 September 2008
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	#[http://dx.doi.org/10.1103/PhysRevLett.78.2690 C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters '''78''' 2690-2693 (1997)]		#[http://dx.doi.org/10.1103/PhysRevLett.78.2690 C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters '''78''' 2690-2693 (1997)]
	#[http://dx.doi.org/10.1080/00268970500151536 E. G. D. Cohen; D. Mauzerall "The Jarzynski equality and the Boltzmann factor", Molecular Physics '''103''' pp. 2923 - 2926 (2005)]		#[http://dx.doi.org/10.1080/00268970500151536 E. G. D. Cohen; D. Mauzerall "The Jarzynski equality and the Boltzmann factor", Molecular Physics '''103''' pp. 2923 - 2926 (2005)]
			#[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: Added internal link

2008-02-06T10:57:34Z

Added internal link

← Older revision		Revision as of 12:57, 6 February 2008
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	{{Stub-general}}		{{Stub-general}}
	The '''Jarzynski equality''' is also known as the ''work relation'' or ''non-equilibrium work relation''.		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>\Delta A</math>, can be reconstructed by averaging the external work, <math>W</math>, performed in many nonequilibrium realizations of the process (Ref. 1 Eq. 2a):		According to this equality, the ''equilibrium'' [[Helmholtz energy function]] of a process, <math>\Delta A</math>, can be reconstructed by averaging the external [[work]], <math>W</math>, performed in many nonequilibrium realizations of the process (Ref. 1 Eq. 2a):
	:<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>

Carl McBride at 10:27, 6 February 2008

2008-02-06T10:27:28Z

← Older revision		Revision as of 12:27, 6 February 2008
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	{{Stub-general}}		{{Stub-general}}
	The '''Jarzynski equality''' is also known as the ''work relation'' or ''non-equilibrium work relation''.		The '''Jarzynski equality''' is also known as the ''work relation'' or ''non-equilibrium work relation''.
	According to this equality, the ''equilibrium'' [[~~Gibbs~~ energy function ~~\|free energy~~]] of a process, <math>\Delta G</math>, can be reconstructed by averaging the external work, <math>W</math>, performed in many nonequilibrium realizations of the process:		According to this equality, the ''equilibrium'' [[Helmholtz energy function]] of a process, <math>\Delta A</math>, can be reconstructed by averaging the external work, <math>W</math>, performed in many nonequilibrium realizations of the process (Ref. 1 Eq. 2a):
	:<math>\exp \left( \frac{-\Delta G}{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>

	where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]].		or can be trivially re-written as (Ref. 1 Eq. 2b)

			:<math>\Delta A = - \frac{1}{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 proof of this equation is given in Ref. 1 and the only assumption is that of a weak coupling between the system and the reservoir.
	==References==		==References==
	#[http://dx.doi.org/10.1103/PhysRevLett.78.2690 C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters '''78''' 2690-2693 (1997)]		#[http://dx.doi.org/10.1103/PhysRevLett.78.2690 C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters '''78''' 2690-2693 (1997)]