Martyna-Tuckerman-Tobias-Klein barostat

Martyna-Tuckerman-Tobias-Klein barostat has the following equations of motion (Eq.13):

${\dot {\mathbf {r} }}_{i}={\frac {{\mathbf {p} }_{i}}{m_{i}}}+{\frac {{\overline {\mathbf {p} }}_{g}}{W_{g}}}{\mathbf {r} }_{i}$

${\dot {\mathbf {p} }}_{i}={\mathbf {F} }_{i}-{\frac {{\overline {\mathbf {p} }}_{g}}{W_{g}}}{\mathbf {p} }_{i}-\left({\frac {1}{N_{f}}}\right){\frac {\mathrm {Tr} [{\overline {\mathbf {p} }}_{g}]}{W_{g}}}-{\frac {p_{\xi }}{Q}}{\mathbf {p} }_{i}$

${\dot {\overline {\mathbf {h} }}}={\frac {{\overline {\mathbf {p} }}_{g}{\overline {\mathbf {h} }}}{W_{g}}}$

${\dot {\overline {\mathbf {p} }}}_{g}=V\left({\overline {\mathbf {p} }}_{\mathrm {int} }-{\overline {\mathbf {I} }}P_{\mathrm {ext} }\right)+\left[{\frac {1}{N_{f}}}\sum _{i=1}^{N}{\frac {{\mathbf {p} }_{i}^{2}}{m_{i}}}\right]{\overline {\mathbf {I} }}-{\frac {p_{\xi }}{Q}}{\overline {\mathbf {p} }}_{g}$

${\dot {\xi }}={\frac {p_{\xi }}{Q}}$

${\dot {p}}_{\xi }=\sum _{i=1}^{N}{\frac {{\mathbf {p} }_{i}^{2}}{m_{i}}}+{\frac {1}{W_{g}}}\mathrm {Tr} \left[{\overline {\mathbf {p} }}_{g}^{t}{\overline {\mathbf {p} }}_{g}\right]-(N_{f}+d^{2})kT$