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Event-Chain Monte Carlo: The global-balance breakthrough

E.A.J.F. (Frank) Peters
Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, The Netherlands

Commentary on

E.P. Bernard, W. Krauth and D.B. Wilson, “Event-chain Monte Carlo algorithms for hard-sphere systems”, Phys. Rev. E, 80:056704 (2009), https://doi.org/10.1103/PhysRevE.80.056704

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Statement of Significance

The seminal 2009 paper by Bernard, Krauth, and Wilson marked a paradigm shift in Monte Carlo sampling. By abandoning the restrictive condition of detailed balance in favor of the more fundamental principle of global balance, they introduced the Event-Chain Monte Carlo (ECMC) algorithm, which achieves rejection-free, deterministic sampling for hard spheres. This breakthrough demonstrated that persistent, directional dynamics could dramatically accelerate equilibration in dense particle systems. In this commentary, we review this foundational work and elucidate its underlying mechanism using the broader Event-Driven Monte Carlo (EDMC) framework developed in subsequent years. We show how the original hard-sphere concept naturally generalizes to continuous potentials and modern lifted Markov chain formalisms, transforming a surprising specific result into a powerful general class of sampling algorithms.

How to cite

Cite the commentary as:

E.A.J.F. Peters, "Event-Chain Monte Carlo: The global-balance breakthrough",
KIM REVIEW, Volume 4, Article 02, 2026. DOI: 10.25950/a25ce9a6