Jarzynski equality: Difference between revisions
Carl McBride (talk | contribs) m (Added internal link) |
Carl McBride (talk | contribs) m (→References: Added a reference) |
||
| Line 11: | Line 11: | ||
#[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]] | ||
Revision as of 14:57, 5 September 2008
|
This article is a 'stub' page, it has no, or next to no, content. It is here at the moment to help form part of the structure of SklogWiki. If you add sufficient material to this article then please remove the {{Stub-general}} template from this page. |
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, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta A} , can be reconstructed by averaging the external work, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W} , performed in many nonequilibrium realizations of the process (Ref. 1 Eq. 2a):
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \exp \left( \frac{-\Delta A}{k_BT}\right)= \left\langle \exp \left( \frac{-W}{k_BT} \right) \right\rangle}
or can be trivially re-written as (Ref. 1 Eq. 2b)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta A = - \frac{1}{k_BT} \ln \left\langle \exp \left( \frac{-W}{k_BT} \right) \right\rangle }
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_B} is the Boltzmann constant and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} 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
- C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters 78 2690-2693 (1997)
- E. G. D. Cohen; D. Mauzerall "The Jarzynski equality and the Boltzmann factor", Molecular Physics 103 pp. 2923 - 2926 (2005)
- L. Y. Chen "On the Crooks fluctuation theorem and the Jarzynski equality", Journal of Chemical Physics 129 091101 (2008)