Molecular Dynamics in the Multicanonical Ensemble: Equivalence of   Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and   Metadynamics
  We show direct formal relationship between the Wang-Landau iteration [PRL 86, 2050 (2001)], metadynamics [PNAS 99, 12562 (2002)] and statistical temperature molecular dynamics [PRL 97, 050601 (2006)], the major Monte Carlo and molecular dynamics work-horses for sampling from a generalized, multicanonical ensemble. We demonstrate that statistical temperature molecular dynamics (which is formally derived from the Wang-Landau method), augmented by the introduction of kernel updates of the statistical temperature, generates dynamics which are indistinguishable from a corresponding metadynamics simulation. We also show that the use of a Gaussian kernel significantly improves the performance of statistical temperature molecular dynamics, highlighting the practical benefits of this improved formal understanding. 
Christoph Junghans, Danny Perez, Thomas Vogel
cond-mat.stat-mech cond-mat.mtrl-sci cond-mat.soft physics.comp-ph