Jarzynski equality

Assuming an infinite number of realizations of the process, equilibrium properties can be obtained from the non-equilibrium dynamics by the Jarzynski equality,... 

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

Equation (16) has appeared in the past in the literature [41, 42] and is mathematically identical to the Jarzynski equality [31]. We analyze this connection in Section III.C.l. 

This relation is called the Jarzynski equality (hereafter referred to as JE) and can be used to recover free energies from nonequilibrium simulations or experiments (see Section IV.B.2). The FT in Eq. (27) becomes the Crooks fluctuation theorem (hereafter referred to as GET) [45, 46] ... 

F. Douarche, S. Ciliberto, and A. Petrosyan, An experimental test of the Jarzynski equality in a mechanical experiment. Eumphys. Lett. 70, 593-598 (2005). 

J. Fiphardt, S. Dumont, S. B. Smith, I. Tinoco, Jr., and C. Bustamante, Equilibrium information from nonequilibrium measurements in an experimental test of the Jarzynski equality. Science 296, 1833-1835 (2002). 

I. Kosztin, B. Barz, and L. Janosi, Calculating potentials of mean force and diffusion coefficients from nonequihbrium processes without Jarzynski equality. J. Chem. Phys. 124, 064106 (2006). 

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... 

Evans and Searles reviewed the transient fluctuation relations, how steady state relations can be derived from them, their implications and applications, and experimental tests available in 2002. A shorter review paper highlighted the main results, and a derivation of the second law inequality. Recently, Sevick et al reviewed the ES FR, the Crooks FR and the Jarzynski equality, highlighting the similarities and differences between the two FRs and also discussing experimental work that has been carried out to test these results. 

Several reviews have focussed on stochastic dynamics. Harris and Schiitz discuss a range of fluctuation theorems (the Jarzynski equality, the ES FR and the GC FR) in the context of stochastic, Markov systems, but in a widely applicable context. They investigate the conditions under which they apply, including an analysis of the conditions under which the GC FR is valid. In 2006, Gaspard reviewed studies where a stochastic approach to the treatment of boundaries is used to obtain FRs for the current in nanosystems, with a focus on work from his group, and also published a review on Hamiltonian systems that includes a discussion on FRs and the JE. 

Recent reviews on the Jarzynski equality and related theorems discuss the method and its application.In section 3.2 we describe recent developments associated with the Crooks FR and JE, citing papers where the different approaches have been used and compared. A special issue of Molecular Simulation Challenges in Free Energy Calculations published in Jan-Feb 2002 includes articles on the different approaches to free energy calculations, including the Jarzynski approach. 

Various groups have developed reweighting and optimisation schemes to improve the converges of the Jarzynski equality (see for examples,212 216). Gore et al.217 examine the finite sampling error for the Jarzynski equality in the nearequilibrium regime, and develop a bias-corrected estimation. 

A number of papers have presented alternative derivations or generalisations of the Jarzynski equality and fluctuation relations, including their application... 

Prom a computational point of view the Jarzynski equality is interesting, because it permits the calculation of free energy differences from simulations in which a control parameter is switched at arbitrary speed. To be more specific, consider a system with Hamiltonian H x, A) depending on the phase space point X and the control parameter A. By changing A continuously from its initial value Aq to its final value Ai the Hamiltonian H x,Xo) of the initial state is transformed into that of the final state H x,Xi). The free energy difference... 

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