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We show direct formal relationship between the Wang-Landau iteration [PRL 86,2050 (2001)], metadynamics [PNAS 99, 12562 (2002)] and statistical temperaturemolecular dynamics [PRL 97, 050601 (2006)], the major Monte Carlo and moleculardynamics work-horses for sampling from a generalized, multicanonical ensemble.We demonstrate that statistical temperature molecular dynamics (which isformally derived from the Wang-Landau method), augmented by the introduction ofkernel updates of the statistical temperature, generates dynamics which areindistinguishable from a corresponding metadynamics simulation. We also showthat the use of a Gaussian kernel significantly improves the performance ofstatistical temperature molecular dynamics, highlighting the practical benefitsof this improved formal understanding.

Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics