Crooks fluctuation theorem

The Crooks fluctuation theorem was developed by Gavin E. Crooks. It is also known as the Crooks Identity or the Crooks fluctuation relation. It is given by ( Eq. 2):

${\frac {P_{F}(+\omega )}{P_{R}(-\omega )}}=\exp({+\omega })$

where $\omega$ is the entropy production, $P_{F}(\omega )$ is the "forward" probability distribution of this entropy production, and $P_{R}(-\omega )$, time-reversed. This expression can be written in terms of work ($W$) (Eq. 11):

${\frac {P_{F}(+\beta W)}{P_{R}(-\beta W)}}=\exp(-\Delta A)\exp(+\beta W)$

where $\beta :=1/(k_{B}T)$ where $k_{B}$ is the Boltzmann constant and $T$ is the temperature, and $A$ is the Helmholtz energy function.

See also

• Jarzynski equality

References

Related reading

• L. Y. Chen "On the Crooks fluctuation theorem and the Jarzynski equality", Journal of Chemical Physics 129 091101 (2008)
• Riccardo Chelli "Nonequilibrium work relations for systems subject to mechanical and thermal changes", Journal of Chemical Physics 130 054102 (2009)