  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.
