Measuring the convergence of Monte Carlo free-energy calculations

Aljoscha M. Hahn, H Then

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)


The nonequilibrium work fluctuation theorem provides the way for calculations of (equilibrium) free-energy based on work measurements of nonequilibrium, finite-time processes, and their reversed counterparts by applying Bennett’s acceptance ratio method. A nice property of this method is that each free-energy estimate readily yields an estimate of the asymptotic mean square error. Assuming convergence, it is easy to specify the uncertainty of the results. However, sample sizes have often to be balanced with respect to experimental or computational limitations and the question arises whether available samples of work values are sufficiently large in order to ensure convergence. Here, we propose a convergence measure for the two-sided free-energy estimator and characterize some of its properties, explain how it works, and test its statistical behavior. In total, we derive a convergence criterion for Bennett’s acceptance ratio method.
Translated title of the contributionMeasuring the convergence of Monte Carlo free-energy calculations
Original languageEnglish
Pages (from-to)041117 - 041128
Number of pages12
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Issue number4
Publication statusPublished - Apr 2010

Bibliographical note

Publisher: American Physical Society


  • free-energy calculations
  • Monte Carlo methods
  • convergence measure


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