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| The '''Andersen thermostat''' was the first thermostat proposed for [[molecular dynamics]], thus permitting one to use the [[canonical ensemble]] (NVT) in simulations. The Andersen thermostat (Ref. <ref>[http://dx.doi.org/10.1063/1.439486 Hans C. Andersen "Molecular dynamics simulations at constant pressure and/or temperature", Journal of Chemical Physics '''72''' pp. 2384-2393 (1980)]</ref>, section IV) couples the system to a heat bath via stochastic forces that modify the kinetic energy of the atoms or molecules.
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| The time between collisions, or the number of collisions in some (short) time interval is decided [[random numbers |randomly]], with the following [[Poisson distribution]] (Eq. 4.1):
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| :<math>P(t) = \nu e^{-\nu t}.</math>
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| where <math>\nu</math> is the stochastic collision frequency.
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| Between collisions the system evolves at constant energy, i.e. business as usual. Upon a 'collision event' the new momentum of the lucky atom (or molecule) is chosen at random from a [[Boltzmann distribution]] at [[temperature]] <math>T</math>.
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| In principle <math>\nu</math> can adopt any value. However, there does exist an optimum choice (Eq. 4.9):
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| :<math>\nu = \frac{2a \kappa V^{1/3}}{3 k_BN} = \frac{2a \kappa}{3 k_B\rho^{1/3}N^{2/3}}</math>
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| where <math>a</math> is a dimensionless constant, <math>\kappa</math> is the [[thermal conductivity]], <math>V</math> is the volume, <math>k_B</math> is the [[Boltzmann constant]], and <math>\rho</math> is the [[number density]] of particles; <math>\rho:=N/V</math>.
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| Note: the Andersen thermostat should only be used for time-independent properties. Dynamic properties, such as the [[diffusion]], should not be calculated if the system is thermostated using the Andersen algorithm <ref>[http://dx.doi.org/10.1063/1.445020 H. Tanaka, Koichiro Nakanishi, and Nobuatsu Watanabe "Constant temperature molecular dynamics calculation on Lennard-Jones fluid and its application to water", Journal of Chemical Physics '''78''' pp. 2626-2634 (1983)]</ref>.
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| ==See also== | | ==See also== |
| *[[Lowe-Andersen thermostat]] | | *[[Lowe-Andersen thermostat]] |
| ==References== | | ==References== |
| <references/>
| | #[http://dx.doi.org/10.1063/1.439486 Hans C. Andersen "Molecular dynamics simulations at constant pressure and/or temperature", Journal of Chemical Physics '''72''' pp. 2384-2393 (1980)] |
| ;Related reading
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| *[http://dx.doi.org/10.1002/cpa.20198 Weinan E and Dong Li "The Andersen thermostat in molecular dynamics", Communications on Pure and Applied Mathematics '''61''' pp. 96-136 (2008)]
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| [[Category: Molecular dynamics]] | | [[Category: Molecular dynamics]] |