Nosé-Hoover thermostat

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)

${\frac {{\mathrm {d} }{\mathbf {v} }(t)}{\mathrm {d} t}}={\frac {{\mathbf {F} }(t)}{m}}-\zeta {\mathbf {v} }(t)$

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \zeta} is the thermodynamic friction coefficient, given by (Ref. 3 Eq. 5)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{{\mathrm {d}}\zeta(t)}{{\mathrm {d}t}} = \frac{1}{Q} \sum m {\mathbf{v}}(t)^2 - (X+1)k_BT}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q} is a parameter that has the dimensions of energy$\times$(time)² and determines the time-scale of the temperature fluctuation and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} is the number of degrees of freedom.

Non-equilibrium

1. Ben Leimkuhler, Frédéric Legoll and Emad Noorizadeh "A temperature control technique for nonequilibrium molecular simulation", Journal of Chemical Physics 128 074105 (2008)

References

1. Shuichi Nosé "A unified formulation of the constant temperature molecular dynamics methods" , Journal of Chemical Physics 81 pp. 511-519 (1984)
2. Shuichi Nosé "A molecular dynamics method for simulations in the canonical ensemble", Molecular Physics 52 pp. 255-268 (1984)
3. William G. Hoover "Canonical dynamics: Equilibrium phase-space distributions", Physical Review A 31 pp. 1695 - 1697 (1985)
4. D. J. Evans and B. L. Holian "The Nose–Hoover thermostat", Journal of Chemical Physics 83 pp. 4069-4074 (1985)