Root mean square fluctuation

The mean square fluctuation (MSF) is a measure of the deviation between the position of particle i and some reference position.

$$MSF=\frac{1}{T}\sum_{t_j=1}^{T}(x_i(t_j) - \tilde{x}_i)^2$$,

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, ie. $$\overline{x}_i$$

Note that where the difference between RMSD and MSF is that with the later the average is taken over time, giving a value for each particle i. With RMSD the average is taken over the particles, giving time specific values.