Position-Momenta Uncertainties in Classical Systems

We show that classical particles in a thermal bath that respects
the angular momentum conservation, or allow the angular momentum to
fluctuate about a nonzero mean, exhibit a Position-Momentum uncertainty
relation similar to Heisenberg uncertainty. For particles in central
potential, irrespective of its form, this relation reduces to $Delta x
 Delta p_x > L/2$ where $L$ is the mean angular momentum (or the initial
angular momentum, in a conserved ensemble). Existence of such thermal
baths are shown by designing Langevin baths, for both conserved and
non-conserved angular momentum ensembles, that maintain a Boltzmann
distribution of energy in the steady state. An experimental realization of
the uncertainty bound will also be  discussed. The talk is aimed at
general Phys audience.