LONGTIME CONVERGENCE OF THE TEMPERATURE-ACCELERATED MOLECULAR DYNAMICS METHOD. Stoltz, G. & Vanden-Eijnden, E. 2017.
LONGTIME CONVERGENCE OF THE TEMPERATURE-ACCELERATED MOLECULAR DYNAMICS METHOD [pdf]Paper  LONGTIME CONVERGENCE OF THE TEMPERATURE-ACCELERATED MOLECULAR DYNAMICS METHOD [pdf]Website  abstract   bibtex   
The equations of the temperature-accelerated molecular dynamics (TAMD) method for the calculations of free energies and partition functions are analyzed. Specif-ically, 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 tem-perature 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 pre-cisely. 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.

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