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## Jarzynski equalityThe ## Additional recommended knowledgeIn thermodynamics, the free energy difference Δ - ,
the equality happening only in the case of a quasistatic process, i.e. when one takes the system from In contrast to the thermodynamic statement above, the JE remains valid no matter how fast the process happens. The equality itself can be straightforwardly derived from the Crooks fluctuation theorem and is presented below, followed by a brief explanation of the terms and notation: Here The over-line indicates an average over all possible realizations of a process that takes the system from the equilibrium state in accordance with the second law of thermodynamics. Since its original derivation, the Jarzynski equality has been verified in a variety of contexts, ranging from experiments with biomolecules to numerical simulations. Many other theoretical derivations have also appeared, lending further confidence to its universality. An issue of current debate is whether the Jarzynski equality was published already in 1977 by the Russian physicists G.N. Bochkov and Yu. E. Kuzovlev (see Bibliography). These authors proposed a generalized version of the Fluctuation-Dissipation relations which holds even in the presence of arbitrary external time-dependent forces. The generalized Fluctuation-Dissipation relations take on a similar form as the more recently proposed fluctuation theorem. ## Notes- The Jarzynski equality actually encompasses more general scenarios where the final state of the system is out of equilibrium. In this case, since free energies are generally defined only for equilibrium states, one has to specify exactly what is the quantity
*F*_{B}that appears on the l.h.s. of the JE. This specification requires a precise definition of the process that takes the system from*A*to*B*, and is beyond the scope of this presentation.
## Bibliography- C. Jarzynski,
*Nonequilibrium equality for free energy differences*, Phys. Rev. Lett.**78**, 2690 (1997) - C. Jarzynski,
*Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach*, Phys. Rev. E**56**, 5018 (1997) - G. E. Crooks,
*Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems*, J. Stat. Phys.**90**, 1481 (1998) - G. Hummer, A. Szabo,
*Free energy reconstruction from nonequilibrium single-molecule pulling experiments*, Proc. Nat. Acad. Sci.**98**, 3658 (2001) - J. Liphardt et al.,
*Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski's equality*, Science**296**, 1832 (2002) - D. J. Evans,
*A non-equilibrium free energy theorem for deterministic systems*, Mol. Phys.**101**, 1551 (2003) - A. B. Adib,
*Entropy and density of states from isoenergetic nonequilibrium processes*, Phys. Rev. E**71**, 056128 (2005) - F. Douarche, S. Ciliberto, A. Petrosyan, I. Rabbiosi,
*An experimental test of the Jarzynski equality in a mechanical experiment*, Europhys. Lett.**70**(**5**), 593 (2005, see also cond-mat/0502395)
- G. N. Bochkov and Yu. E. Kuzovlev, Zh. Eksp. Teor. Fiz.
**72**, 238 (1977);*op. cit.***76**, 1071 (1979) - G. N. Bochkov and Yu. E. Kuzovlev, Physica
**106A**, 443 (1981);*op. cit.***106A**, 480 (1981)
## See also- Fluctuation theorem - Provides an equality that quantifies fluctuations in time averaged entropy production in a wide variety of nonequilibrium systems.
- Jarzynski equality on arxiv.org
Categories: Statistical mechanics | Non-equilibrium thermodynamics |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Jarzynski_equality". A list of authors is available in Wikipedia. |