Error Analysis in Molecular Dynamics Simulation
In molecular dynamics (MD) simulations, there are errors due to inadequate sampling of the phase space or infrequently occurring events, these lead to the statistical error due to random fluctuation in the measurements.
For a series of M measurements of a fluctuating property A, the mean value is:
When these M measurements are independent, the variance of the mean <A> is:
but in most MD simulations, there is correlation between quantity A at different time, so the variance of the mean <A> will be underestimated as the effective number of independent measurements is actually less than M. In such situations we rewrite the variance as :
where is the autocorrelation function defined by
We can then use the autocorrelation function to estimate the error bar. Luckily, we have a much simpler method based on block averaging.
Read more about this topic: Error Analysis
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