ICTS

We demonstrate that classical particles coupled to thermal baths that conserve angular momentum, or allow it to fluctuate about a nonzero mean, obey a position–momentum uncertainty relation formally analogous to the Heisenberg bound. For motion in an arbitrary central potential, this relation universally reduces to  ΔxΔpx>L/2  where  L is the mean angular momentum (or the conserved initial value). We establish the physical realizability of such baths by constructing Langevin dynamics that preserve a Boltzmann energy distribution in steady state for both conserved and non-conserved angular momentum ensembles. We also outline experimental routes for observing this emergent classical uncertainty bound.
Ref: Dipesh K. Singh and  PKM, Phys. Rev. E 112, 054129 (2025).