Crooks fluctuation theorem

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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 ([1] 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_BT) where k_B is the Boltzmann constant and T is the temperature, and A is the Helmholtz energy function.

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