Jarzynski equality: Difference between revisions

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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]]

Revision as of 18:29, 11 March 2010

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, , can be reconstructed by averaging the external work, , performed in many nonequilibrium realizations of the process (Ref. 1 Eq. 2a):

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

where is the Boltzmann constant and 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

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

Related reading