Observation of super-ballistic Brownian motion in liquid
Abstract
Brownian motion is a foundational physical process characterized by a mean squared displacement that scales linearly in time in thermal equilibrium, known as diffusion. At short times, the mean squared displacement becomes ballistic, scaling as [Formula: see text]. This effect was predicted by Einstein in 1907 and recently observed experimentally. We report that this picture is only true on average; by conditioning specific initial velocities, we predict theoretically and confirm by experiment that the mean squared displacement becomes super-ballistic, with a power scaling law of [Formula: see text]. This result is due to the colored noise of incompressible fluids, resulting in a nonzero first moment for the thermal force when conditioned on nonzero initial velocities. These results are a step toward the unraveling of nonequilibrium dynamics of fluids.
Fields of Study & Subjects
stochastic dynamics and bifurcation
Advanced Thermodynamics and Statistical Mechanics
Theoretical and Computational Physics
Publication details
- Journal / source
- Science Advances
- Publisher
- American Association for the Advancement of Science (AAAS)
- Volume
- 12
- Issue
- 6
- Pages
- eaeb4579–eaeb4579
- Publication date
- 4 February 2026
- Language
- EN