  The equations of the temperature-accelerated molecular dynamics (TAMD) method
for the calculations of free energies and partition functions are analyzed.
Specifically, the exponential convergence of the law of these stochastic
processes is established, with a convergence rate close to the one of the
limiting, effective dynamics at higher temperature obtained with infinite
acceleration. It is also shown that the invariant measures of TAMD are close to
a known reference measure, with an error that can be quantified precisely.
Finally, a Central Limit Theorem is proven, which allows the estimation of
errors on properties calculated by ergodic time averages. These results not
only demonstrate the usefulness and validity range of the TAMD equations, but
they also permit in principle to adjust the parameter in these equations to
optimize their efficiency.
