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 $\zeta$ is the thermodynamic friction coefficient, given by (Ref. 3 Eq. 5)

${\frac {{\mathrm {d} }\zeta (t)}{\mathrm {d} t}}={\frac {1}{Q}}\left[\sum m{\mathbf {v} }(t)^{2}-(X+1)k_{B}T\right]$

where $Q$ is a parameter that has the dimensions of energy$\times$(time)² and determines the time-scale of the temperature fluctuation and $X$ is the number of degrees of freedom.

Problems

The Nosé-Hoover thermostat has problems with ergodicity for small or stiff systems. In order to compensate for this a modification using "chains" has been proposed .

Non-equilibrium

A version of the Nosé-Hoover thermostat has been developed for non-equilibrium simulations .

References

Related reading

• 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)
• See http://williamhoover.info and Wm. G. Hoover and Carol G. Hoover, Time Reversibility, Computer Simulations, Algorithms, Chaos (World Scientific, Singapore, 2012).