Nosé-Hoover thermostat

2014-04-04T02:10:44Z

67.54.210.3: /* References */

The '''Nosé-Hoover thermostat'''<ref>[http://dx.doi.org/10.1063/1.447334 Shuichi Nosé "A unified formulation of the constant temperature molecular dynamics methods" , Journal of Chemical Physics '''81''' pp. 511-519 (1984)]</ref>
<ref>[http://dx.doi.org/10.1080/00268978400101201 Shuichi Nosé "A molecular dynamics method for simulations in the canonical ensemble", Molecular Physics '''52''' pp. 255-268 (1984)]</ref>
<ref>[http://dx.doi.org/10.1103/PhysRevA.31.1695 William G. Hoover "Canonical dynamics: Equilibrium phase-space distributions", Physical Review A '''31''' pp. 1695-1697 (1985)]</ref> is a method for controlling the [[temperature]] in a [[molecular dynamics]] simulation.
The Nosé-Hoover [[thermostats |thermostat]] "strives" to reproduce the [[Canonical ensemble |canonical]] phase-space distribution. It does this by modifying the equations of motion to include a non-Newtonian term in order to maintain the total kinetic energy constant.
The modified equation of motion is given by (Ref. 3 Eq. 4)

:<math>\frac{{\mathrm {d}}{\mathbf{v}}(t)}{{\mathrm {d}t}} = \frac{{\mathbf {F}}(t)}{m} -\zeta {\mathbf{v}}(t)</math>

where <math>\zeta</math> is the thermodynamic friction coefficient, given by (Ref. 3 Eq. 5)

:<math>\frac{{\mathrm {d}}\zeta(t)}{{\mathrm {d}t}} = \frac{1}{Q} \left[ \sum m {\mathbf{v}}(t)^2 - (X+1)k_BT \right]</math>

where <math>Q</math> is a parameter that has the dimensions of energy<math>\times</math>(time)<sup>2</sup> and determines the time-scale of the temperature fluctuation and <math>X</math> is the number of degrees of freedom.
==Problems==
The Nosé-Hoover thermostat has problems with [[Ergodic hypothesis |ergodicity]] for small or stiff systems. In order to compensate for this a modification using "chains" has been proposed <ref>[http://dx.doi.org/10.1063/1.463940 Glenn J. Martyna, Michael L. Klein and Mark Tuckerman "Nosé–Hoover chains: The canonical ensemble via continuous dynamics", Journal of Chemical Physics '''97''' pp. 2635- (1992)]</ref>.
==Non-equilibrium==
A version of the Nosé-Hoover thermostat has been developed for [[Non-equilibrium thermodynamics | non-equilibrium]] simulations <ref>[http://dx.doi.org/10.1063/1.2829869 Ben Leimkuhler, Frédéric Legoll and Emad Noorizadeh "A temperature control technique for nonequilibrium molecular simulation", Journal of Chemical Physics '''128''' 074105 (2008)]</ref>.
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1063/1.449071 D. J. Evans and B. L. Holian "The Nose–Hoover thermostat", Journal of Chemical Physics '''83''' pp. 4069-4074 (1985)]
*[http://dx.doi.org/10.1063/1.2013227 Carlos Braga and Karl P. Travis "A configurational temperature Nosé-Hoover thermostat", Journal of Chemical Physics '''123''' 134101 (2005)]
* See http://williamhoover.info and Wm. G. Hoover and Carol G. Hoover, Time Reversibility, Computer Simulations, Algorithms, Chaos (World Scientific, Singapore, 2012).
[[category: molecular dynamics]]

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Nosé-Hoover thermostat