Abstract
Systematic inaccuracy is inherent in any computational estimate of a nonlinear average, due to the availability of only a finite number of data values, . Free energy differences 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 —in 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 for large , the identification of a universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems.
- Received 12 March 2002
DOI:https://doi.org/10.1103/PhysRevLett.89.180602
©2002 American Physical Society