Jarzynski equality: Difference between revisions
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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'' [[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: | ||
:<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 G}{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]]. | |||
==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)] | ||
Revision as of 11:27, 5 February 2008
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The Jarzynski equality is also known as the work relation or non-equilibrium work relation. According to this equality, the equilibrium free energy 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 G} , 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:
- 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 G}{k_BT}\right)= \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.