Jarzynski equality: Difference between revisions

Revision as of 13:44, 15 June 2011

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, ( $A$ ), can be reconstructed by averaging the external work, $W$ , performed in many non-equilibrium realizations of the process (Eq. 2a in ^[1]):

\exp \left({\frac {-\Delta A}{k_{B}T}}\right)=\left\langle \exp \left({\frac {-W}{k_{B}T}}\right)\right\rangle

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

\Delta A=-k_{B}T\ln \left\langle \exp \left({\frac {-W}{k_{B}T}}\right)\right\rangle

where $k_{B}$ is the Boltzmann constant and $T$ 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

↑ C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters 78 2690-2693 (1997)

Related reading

[1] C. Jarzynski "Nonequilibrium Equality for Free Energy Differences", Physical Review Letters 78 2690-2693 (1997)

[1]

@@ Line 1: / Line 1: @@
 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>
-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==
-#[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'''
 *[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)]

Jarzynski equality: Difference between revisions

Revision as of 13:44, 15 June 2011

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