  Fast and accurate sampling method is in high demand, in order to bridge the
large gaps between molecular dynamic simulations and experimental observations.
Recently, integrated tempering enhanced sampling method (ITS) has been proposed
and successfully applied to various biophysical examples, significantly
accelerating conformational sampling. The mathematical validation for its
effectiveness has not been elucidated yet. Here we show that the integrated
tempering enhanced sampling method can be viewed as a reformulation of the
infinite switching limit of simulated tempering method over a mixed potential.
Moreover, we demonstrate that the efficiency of simulated tempering molecular
dynamics (STMD) improves as the frequency of switching between the temperatures
is increased, based on the large deviation principle of empirical
distributions. Our theory provides the theoretical justification of the
advantage of ITS. Finally, we illustrate the utility of the infinite switching
simulated tempering method through several numerical examples.

Numerical Analysis;Chemical Physics;Computational Physics