# Root mean square fluctuation

$MSF=\sqrt{\frac{1}{T}\sum_{t_j=1}^{T}(x_i(t_j) - \tilde{x}_i)^2}$,
where T is the time over which one wants to average, and $\tilde{x}_i$ is the reference position of particle i. Typically this reference position will be the time-averaged position of the same particle i, i.e. $\overline{x}_i$