Nosé-Hoover thermostat: Difference between revisions
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where <math>\zeta</math> is the thermodynamic friction coefficient, given by (Ref. 3 Eq. 5) | 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} \sum m {\mathbf{v}}(t)^2 - (X+1)k_BT</math> | :<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. | 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. | ||
Revision as of 16:30, 26 March 2008
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The Nosé-Hoover thermostat is a method for controlling the temperature in a molecular dynamics simulation. The Nosé-Hoover thermostat "strives" to reproduce the 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)
where is the thermodynamic friction coefficient, given by (Ref. 3 Eq. 5)
![{\displaystyle {\frac {{\mathrm {d} }\zeta (t)}{\mathrm {d} t}}={\frac {1}{Q}}\left[\sum m{\mathbf {v} }(t)^{2}-(X+1)k_{B}T\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/039cc14a8a6a5471a4c428e173d1287bbf4a4a87)
where is a parameter that has the dimensions of energy(time)2 and determines the time-scale of the temperature fluctuation and is the number of degrees of freedom.
Non-equilibrium
References
- Shuichi Nosé "A unified formulation of the constant temperature molecular dynamics methods" , Journal of Chemical Physics 81 pp. 511-519 (1984)
- Shuichi Nosé "A molecular dynamics method for simulations in the canonical ensemble", Molecular Physics 52 pp. 255-268 (1984)
- William G. Hoover "Canonical dynamics: Equilibrium phase-space distributions", Physical Review A 31 pp. 1695 - 1697 (1985)
- D. J. Evans and B. L. Holian "The Nose–Hoover thermostat", Journal of Chemical Physics 83 pp. 4069-4074 (1985)
- Carlos Braga and Karl P. Travis "A configurational temperature Nosé-Hoover thermostat", Journal of Chemical Physics 123 134101 (2005)