# softmatter:Autocorelation function

### From NSDL Materials Digital Library Wiki

An autocorrelation function indicates the extent to which a system retains a “memory” of itself at a previous time (or, conversely, how long it takes the system to “lose” its memory and “decorrelate” from itself.) The autocorrelation function for a particular property tells you how long you must simulate to generate a series of configurations uncorrelated from the previous series with respect to that property.

- In many instances, autocorrelation functions decay exponentially: C(t) = exp(t/τC)
- Then the relaxation time is typically the time it takes for the function to fall to 1/e of its initial value.
- It is possible to construct an autocorrelation function for any particle quantity (e.g. v
_{i}, u_{i},...) or any system quantity (e.g. U, E ...).

The general formulation is:

where A is the quantity of interest.