Mean squared displacement (MSD) is a statistical measure used to evaluate the average squared displacement of particles or objects over time. It is commonly employed in fields such as physics, chemistry, and biophysics to analyze the motion of particles in a variety of systems, including gases, liquids, and biological systems.
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A mean squared displacement is the expected value of a squared position change over a specified time lag. For isotropic free diffusion in dimensions, it equals . A nonzero mean drift contributes its squared displacement as well as the displacement variance; specifying the tracked coordinates and whether the mean is subtracted is essential.