I am calculating the viscosity of WCA fluid using the Green-Kubo relation. I am also following the paper of Zhang et al. for the Time decomposition method where they fit an analytic function to the running integral of Green Kubo. To do that it is suggested to run multiple short runs with different initial conditions, calculate the Green-Kubo running integral for each of those runs. Then calculate the mean and standard deviation across those runs to obtain a time series data for mean and standard deviation.

What I found for WCA (they did for molecular systems) is that the standard deviation curve is an increasing function, roughly as $t^{\frac{1}{2}}$. I was wondering why is that so. Is it occurring due to statistical reasons or some deeper physics is involved? Below is the standard deviation across multiple independent runs. The standard deviation is fitted to a power law $Ct^b$ and $b \sim 0.5$

  • $\begingroup$ WCA = Weeks-Chandler-Andersen? It's good practice to define any acronyms you use. $\endgroup$
    – Ian Bush
    May 13 at 13:45
  • $\begingroup$ Yes. This is pretty common notation I have come across in the field. So I assumed it is not required. But I will keep this in mind for future $\endgroup$ May 13 at 17:36
  • $\begingroup$ A standard deviation increasing in time like $\sqrt t$ just makes me think Brownian motion but that could just be nonsensical free association... $\endgroup$ May 14 at 4:08
  • $\begingroup$ @DanielShapero I think there could be some hidden connection though. $\endgroup$ May 15 at 5:56


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