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The Andersen thermostat in molecular dynamics
Author(s) -
E Weinan,
Li Dong
Publication year - 2008
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20198
Subject(s) - thermostat , ergodic theory , diffusion , statistical physics , mathematics , convergence (economics) , limit (mathematics) , constant (computer programming) , mathematical analysis , thermodynamics , physics , computer science , economics , economic growth , programming language
We carry out a mathematical study of the Andersen thermostat [1], which is a frequently used tool in molecular dynamics. After reformulating the continuous‐ and discrete‐time Andersen dynamics, we prove that in both cases the Andersen dynamics is uniformly ergodic. A detailed numerical analysis is presented, establishing the rate of convergence of most commonly used numerical algorithms for the Andersen thermostat. Transport properties such as the diffusion constant are also investigated. It is proved for the Lorentz gas model where there is intrinsic diffusion that the diffusion coefficient calculated using the Andersen thermostat converges to the true diffusion coefficient in the limit of vanishing collision frequency in the Andersen thermostat. © 2007 Wiley Periodicals, Inc.