# Difference between revisions of "Martyna-Tuckerman-Tobias-Klein barostat"

Martyna-Tuckerman-Tobias-Klein barostat [1] [2] has the following equations of motion (Eq.13):

$\dot{\mathbf {r}}_i = \frac{{\mathbf {p}}_i}{m_i} + \frac{\overline{\mathbf {p}}_g}{W_g} {\mathbf {r}}_i$
$\dot{\mathbf {p}}_i = {\mathbf {F}}_i - \frac{\overline{\mathbf {p}}_g}{W_g} {\mathbf {p}}_i - \left(\frac{1}{N_f}\right) \frac{\mathrm{Tr}[ \overline{\mathbf {p}}_g ]}{W_g} - \frac{p_{\xi}}{Q} {\mathbf {p}}_i$
$\dot{\overline{\mathbf {h}}} = \frac{\overline{\mathbf {p}}_g {\overline{\mathbf {h}}} }{W_g}$
$\dot{\overline{\mathbf {p}}}_g = V \left({\overline{\mathbf {p}}}_{\mathrm {int}} - {\overline{\mathbf {I}}} P_{\mathrm {ext}} \right) + \left[ \frac{1}{N_f} \sum_{i=1}^N \frac{{\mathbf {p}}_i^2 }{m_i} \right] {\overline{\mathbf {I}}} - \frac{p_{\xi}}{Q}{\overline{\mathbf {p}}}_g$
$\dot\xi= \frac{p_{\xi}}{Q}$
$\dot p_{\xi} = \sum_{i=1}^N \frac{{\mathbf {p}}_i^2 }{m_i} + \frac{1}{W_g} \mathrm{Tr}\left[ {\overline{\mathbf {p}}}_g^t {\overline{\mathbf {p}}}_g \right] - (N_f + d^2) kT$