Jarzynski equality: Difference between revisions

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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>\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>



Revision as of 11:57, 6 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 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)
  2. E. G. D. Cohen; D. Mauzerall "The Jarzynski equality and the Boltzmann factor", Molecular Physics 103 pp. 2923 - 2926 (2005)