Editing Jarzynski equality

The '''Jarzynski equality''', also known as the ''work relation'' or ''non-equilibrium work relation'' was developed by Chris Jarzynski.
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  Chris 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 (Eq. 2b)

:<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 only assumption in the proof of this relation is that of a weak coupling between the system and the reservoir. More recently Jarzynski has re-derived this formula, dispensing with this assumption <ref>[http://dx.doi.org/10.1088/1742-5468/2004/09/P09005 Chris Jarzynski "Nonequilibrium work theorem for a system strongly coupled to a thermal environment", Journal of Statistical Mechanics: Theory and Experiment P09005 (2004)]</ref>.
==See also==
*[[Crooks fluctuation theorem]]
==References== 
<references/>
'''Related reading'''
*[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)]
*[http://dx.doi.org/10.1088/0143-0807/31/5/012 Humberto Híjar and José M Ortiz de Zárate "Jarzynski's equality illustrated by simple examples", European Journal of Physics '''31''' pp. 1097 (2010)]
*[http://dx.doi.org/10.1016/j.crhy.2007.04.010 Christopher Jarzynski "Comparison of far-from-equilibrium work relations", Comptes Rendus Physique '''8''' pp. 495-506 (2007)]


[[category: Non-equilibrium thermodynamics]]
[[category: fluctuation theorem]]