  We show that observing the trajectories of confined particles in a thermal
equilibrium state yields an estimate on the free-space diffusion coefficient.
For generic trapping potentials and interactions between particles, the
estimate comes in the form of a lower bound on the true diffusion coefficient.
For non-interacting particles in harmonic trapping potentials, which
approximately describes many experimental situations, the estimate is
asymptotically exact. This allows to determine the diffusion coefficient from
an equilibrium measurement, as opposed to a direct observation of diffusion,
which necessarily starts from a non-equilibrium state. We explicitly
demonstrate that the estimate remains quantitatively accurate in the presence
of weak interactions and anharmonic corrections.

Statistical Mechanics