Berendsen thermostat

The Berendsen thermostat 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 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 \lambda {\mathbf {v}}} , where (Ref. 1 Eq. 11)

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

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

See also

• Bussi-Donadio-Parrinello thermostat