Systematic inaccuracy is inherent in any computational estimate of a nonlinear average, due to the availability of only a finite number of data values, [Formula presented]. Free energy differences [Formula presented] between two states or systems are critically important examples of such averages. Previous work has demonstrated, empirically, that the “finite-sampling error” can be very large—many times [Formula presented]—in [Formula presented] estimates for simple molecular systems. Here we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of [Formula presented] for large [Formula presented], the identification of a universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems. © 2002 The American Physical Society.
CITATION STYLE
Zuckerman, D. M., & Woolf, T. B. (2002). Theory of a Systematic Computational Error in Free Energy Differences. Physical Review Letters, 89(18). https://doi.org/10.1103/PhysRevLett.89.180602
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