Rare events and the convergence of exponentially averaged work values

Details Rare events and the convergence of exponentially averaged work values Rare events and the convergence of exponentially averaged work values

2006-03-07

arxiv.org/abs/cond-mat/0603185v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, including 6 figures

Scientific paper

10.1103/PhysRevE.73.046105

Equilibrium free energy differences are given by exponential averages of nonequilibrium work values; such averages, however, often converge poorly, as they are dominated by rare realizations. I show that there is a simple and intuitively appealing description of these rare but dominant realizations. This description is expressed as a duality between ``forward'' and ``reverse'' processes, and provides both heuristic insights and quantitative estimates regarding the number of realizations needed for convergence of the exponential average. Analogous results apply to the equilibrium perturbation method of estimating free energy differences. The pedagogical example of a piston and gas [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B vol. 109, p. 6805 (2005)] is used to illustrate the general discussion.

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