Root mean square fluctuation
In statistical mechanics, the mean squared displacement (MSD, also mean square displacement, average squared displacement, or mean square fluctuation) is a measure of the deviation time between the position of a particle and some reference position. It is the most common measure of the spatial extent of random motion, and can be thought of as measuring the portion of the system "explored" by the random walker. It prominently appears in the Debye–Waller factor (describing vibrations within the solid state) and in the Langevin equation (describing diffusion of a Brownian particle). The MSD is defined as
where N is the number of particles to be averaged, is the reference position of each particle, is the position of each particles in determined time t.
The probability density function (PDF) for a particle in one dimension is found by solving the one-dimensional diffusion equation. (This equation states that the position probability density diffuses out over time - this is the method used by Einstein to describe a Brownian particle. Another method to describe the motion of a Brownian particle was described by Langevin, now known for its namesake as the Langevin equation.)
...
Wikipedia