Berendsen thermostat

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The Berendsen thermostat [1] is a method for controlling the temperature in a molecular dynamics simulation. The Berendsen thermostat uses a weak coupling (\gamma_i) to an external heat bath of temperature T_0. This results in the modified equation of motion (Ref. 1 Eq. 8):

m_i \frac{{\mathrm d} {\mathbf {v}}_i}{{\mathrm d} t} = {\mathbf {F}}_i + m_i \gamma \left( \frac{T_0}{T} -1\right){\mathbf {v}}_i .

This represents a proportional scaling of the velocities per time step from {\mathbf {v}} to \lambda {\mathbf {v}}, where (Ref. 1 Eq. 11)

\lambda = \left[1 + \frac{\Delta t}{\tau_T} \left( \frac{T_0}{T} -1\right)\right]^{1/2}

where \tau_T is a time constant associated with the coupling.

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