Jarzynski relationship

One of the most important theoretical developments of the last decade is due to Chris Jarzynski, who established a remarkably simple relationship between the equilibrium free energy difference and an ensemble of properly constructed irreversible... 

This can be concluded from the Jarzynski equality (in the distribution function form) and the relationship between the / and g distributions. To repeat... 

Over the past 15 years a number of important fundamental theorems in nonequilibrium statistical mechanics of many-particle systems have been proved. These proofs result in a number of important relations in nonequilibrium statistical mechanics. In this review we focus on three new relationships the dissipation function or Evans-Searles fluctuation relation (ES the Jarzynski equality... 

More recently, Carberry et were able to experimentally demonstrate that the so-called Kawasaki function , that is (e ) = 1 for any time, t, when the system is initially at equilibrium. This follows directly from the fluctuation relation and is also discussed in ref. 70. This relationship suffers from similar difficulties in convergence as do the integrated fluctuation relation and Jarzynski relation (see discussion below), with rare trajectories with negative values of Q, needing to be properly sampled. It therefore serves as a useful experimental control to provide an indication of the level of sampling required for the integrated fluctuation relation and Jarzynski relation to converge. 

Horowitz and Jarzynski examine the connection between a result by Bochkov and Kuzovlev that can be used to obtain an FR, the Crooks FR and the ES FR. They show that the relationships differ in their definition of the work and range of applicability. 

Adib " determined a fluctuation relation for the free energy difference between two constrained configurations i.e. with q fixed at qA and then at qg) by allowing the two different constrained configurations to relax to equilibrium. As noted in that work, this relationship is fundamentally different to Crooks (Jarzynski) because no work is performed during the process. The FR is given by... 

The Jarzynski relation (Eqn (15.39)) is also valid for regimes far from equilibrium. This is the relationship between the difference in free energies of two eqndibrium ensembles AG and the work IT expended in switching between ensembles in a finite time satisfies... 

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