  Spatial multiscale methods have established themselves as useful tools for
extending the length scales accessible by conventional statics (i.e., zero
temperature molecular dynamics). Recently, extensions of these methods, such as
the finite-temperature quasicontinuum (hot-QC) or Coarse-Grained Molecular
Dynamics (CGMD) methods, have allowed for multiscale molecular dynamics
simulations at finite temperature. Here, we assess the quality of the long-time
dynamics these methods generate by considering canonical transition rates.
Specifically, we analyze the transition state theory (TST) rates in CGMD and
compare them to the corresponding TST rate of the fully atomistic system. The
ability of such an approach to reliably reproduce the TST rate is verified
through a relative error analysis, which is then used to highlight the major
contributions to the error and guide the choice of degrees of freedom. Finally,
our analytical results are compared with numerical simulations for the case of
a 1-D chain.
