# Practical way to reduce pressure fluctuations in molecular dynamics? [closed]

I am running a test setup in LAMMPS. I am using $$4000$$ atom hcp system with MEAM potential. The system need to be at equilibrium at $$\pu{10K}$$ and for this I am giving initial velocity at $$\pu{10K}$$ and running NVE for short duration of $$\pu{2ps}$$ ($$\pu{1fs}$$ timestep) followed by NPT at $$\pu{10K}$$ for $$\pu{20ps}$$. I want a configuration where system is at $$\pu{10K}$$ with low pressure.

## Step 1: NVE for short time

Input

velocity all create 10 4928459
fix 1 all nve
run 20000


Output

    Step      Temp         TotEng       Press
18500    4.9325929   -6191.5587    135.54744
19000    5.0476045   -6191.5587    134.10653
19500    5.0523007   -6191.5588    133.15733
20000    5.1187478   -6191.5588    132.81736
20010    5.0694554   -6191.5587    133.90782


Final output is as expected and system equlibrated at $$\pu{5K}$$ as we started with initial velocity of $$\pu{10K}$$ and $$\pu{133bar}$$ of pressure.

## Step 2: NPT

Input

fix 1 all npt temp 10 10 0.1 iso 0.0 0.0 1
run 200000


Output

    Step      Temp         TotEng       Press
217000     10.04384   -6186.4403    157.98486
217500    9.7292229   -6186.5088   -11.700501
218000    9.7728786   -6186.3937   -92.777014
218500    10.165017   -6186.3155   -69.765655
219000     9.875577   -6186.5188   -10.970014
219500    9.9095766   -6186.5424    74.030269
220000    10.251927   -6186.3377    182.70663
220010    10.259622   -6186.3333     76.85412


Here I used Tdamp of $$100\times \text{timestep}$$ and Pdamp of $$1000\times \text{timestep}$$. I have changed different Pdamp value also and found that pressure varies from $$\pu{-200 bar}$$ to $$\pu{+200 bar}$$. (Note for Non-LAMMPS users, the damp parameters give the amount of time for that property to relax).

I can suppress this fluctuation by introducing drag term to Nose-Hoover equation:

Input

fix 1 all npt temp 10 10 0.1 iso 0.0 0.0 1 drag 1


Output

    Step      Temp         TotEng       Press
39000    10.074096   -6186.3848   0.88364453
39500    10.001291   -6186.3747   0.29228989
40000    9.9810361   -6186.3857  -0.12452421
40010    9.7588549    -6186.392  -0.91715159


But I want to suppress these fluctuation in pressure only using real ensemble (with no drag). I tried to increase further run to $$\pu{100 ps}$$, but I can still see fluctuations. How much fluctuation in pressure is acceptable, as these fluctuations increase with temperature also? Any further insight is highly appreciated.