Update fix_press_langevin.rst to include full equation 13

Completest equation 13 to match the [paper](https://pubs.aip.org/jcp/article/141/19/194108/152571/Constant-pressure-and-temperature-discrete-time) and the [implementation](36e739b734/src/fix_press_langevin.cpp (L485-L487)).
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lasergyro
2025-02-18 17:15:01 +01:00
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parent 36e739b734
commit f5099b7c16

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@ -54,7 +54,7 @@ the Langevin equation such as:
f_P = & \frac{N k_B T_{target}}{V} + \frac{1}{V d}\sum_{i=1}^{N} \vec r_i \cdot \vec f_i - P_{target} \\
Q\ddot{L} + \alpha{}\dot{L} = & f_P + \beta(t)\\
L^{n+1} = & L^{n} + bdt\dot{L}^{n} \frac{bdt^{2}}{2Q} \\
L^{n+1} = & L^{n} + bdt\dot{L}^{n} + \frac{bdt^{2}}{2Q} f^{n}_{P} + \frac{bdt}{2Q} \beta^{n+1} \\
\dot{L}^{n+1} = & \alpha\dot{L}^{n} + \frac{dt}{2Q}\left(a f^{n}_{P} + f^{n+1}_{P}\right) + \frac{b}{Q}\beta^{n+1} \\
a = & \frac{1-\frac{\alpha{}dt}{2Q}}{1+\frac{\alpha{}dt}{2Q}} \\
b = & \frac{1}{1+\frac{\alpha{}dt}{2Q}} \\