Berendsen thermostat
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The Berendsen thermostat is a method for controlling the temperature in a molecular dynamics simulation. The Berendsen thermostat uses a weak coupling 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 (\gamma_i)} to an external heat bath of temperature 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 T_0} . This results in the modified equation of motion (Ref. 1 Eq. 8):
- 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 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 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 {\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 (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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.