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Nosé-Hoover thermostat

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The Nosé-Hoover thermostat[1] [2] [3] 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_BT \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.


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 [4].


A version of the Nosé-Hoover thermostat has been developed for non-equilibrium simulations [5].


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