期刊
JOURNAL OF STATISTICAL PHYSICS
卷 114, 期 5-6, 页码 1303-1323出版社
KLUWER ACADEMIC/PLENUM PUBL
DOI: 10.1023/B:JOSS.0000013961.84860.5b
关键词
Jensen's inequality; finite-sampling error; systematic error; free energy computation; nonlinear averages
Systematic inaccuracy is inherent in any computational estimate of a non-linear average, such as the free energy difference DeltaF between two states or systems, because of the availability of only a finite number of data values, N. In previous work, we outlined the fundamental statistical description of this finite-sampling error.'' We now give a more complete presentation of (i) rigorous general bounds on the free energy and other nonlinear averages, which generalize Jensen's inequality; ( ii) asymptotic N --> infinity expansions of the average behavior of the finite-sampling error in DeltaF estimates; ( iii) illustrative examples of large-N behavior, both in free-energy and other calculations; and (iv) the universal, large-N relation between the average finite-sampling error and the fluctuation in the error. An explicit role is played by Levy and Gaussian limiting distributions.
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