I am trying to calculate some hydrodynamic properties from MD results. Part of the process in to calculate the transvers current correlation function which is formulated as C(q,t)=⟨J∗(0)J(t)⟩
. The issue is that this formula is regarded as canonical ensemble average in literature which should be calculated based on parameter $\Beta$. However my intuition is that this should be a form of autocorrelation or cross correlation of a rolling window. This is confusing to me and I would like to ask if anyone can provide me a pseudo code example for this calculation.
I think your intuition is correct.
First of all, in equilibrium the ensembles should be equivalent so whether you have a canonical ensemble (fixed temperature) or a microcanonical ensemble (fixed energy, easier in MD) should not matter to zeroth order (apart from subtle finite size effects that you may worry about much later).
Then the average is, as you say, just an average over snapshots of the simulation. You need to be careful about the 'rolling window' because ideally you do not want to average over correlated snapshots so you should wait between snapshots until correlations have decayed. Which is a bit of a chicken and egg problem as you want to measure the correlations exactly to figure out how long they persist. So this probably needs some iterations to figure out good parameters. Or, alternatively, you do not reuse simulations at all and start from fresh, random initial conditions for every t=0.
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