Longtime convergence of the temperature-accelerated molecular dynamics method

Gabriel Stoltz, Eric Vanden Eijnden

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)3748-3769
Number of pages22
JournalNonlinearity
Volume31
Issue number8
DOIs
StatePublished - Jul 4 2018

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Molecular Dynamics
Molecular dynamics
molecular dynamics
Exponential Convergence
stochastic processes
Time-average
Energy Function
Dynamic Equation
Invariant Measure
Partition Function
Central limit theorem
Temperature
temperature
Convergence Rate
Stochastic Processes
Free Energy
partitions
theorems
Limiting
Random processes

Keywords

  • longtime convergence
  • molecular dynamics
  • Poisson equation
  • stochastic differential equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Longtime convergence of the temperature-accelerated molecular dynamics method. / Stoltz, Gabriel; Vanden Eijnden, Eric.

In: Nonlinearity, Vol. 31, No. 8, 04.07.2018, p. 3748-3769.

Research output: Contribution to journalArticle

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