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Martyna-Tuckerman-Tobias-Klein barostat

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Martyna-Tuckerman-Tobias-Klein barostat [1] [2] 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