Systematic finite-sampling inaccuracy in free energy differences and other nonlinear quantities

Daniel M. Zuckerman, Thomas B. Woolf

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


Systematic inaccuracy is inherent in any computational estimate of a non-linear average, such as the free energy difference ΔF 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 → ∞ expansions of the average behavior of the finite-sampling error in ΔF 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 Lévy and Gaussian limiting distributions.

Original languageEnglish (US)
Pages (from-to)1303-1323
Number of pages21
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Mar 2004
Externally publishedYes


  • Finite-sampling error
  • Free energy computation
  • Jensen's inequality
  • Nonlinear averages
  • Systematic error

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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