Possible Enhancements of Collective Flow Anisotropy Induced by Uncertainty Relation for Fluid Element

In the stochastic formulation of viscous hydrodynamics, the velocity of a fluid element fluctuates satisfying a similar relation to the quantum-mechanical uncertainty relation. Using a non-relativistic toy model, we show that the presence of such a velocity fluctuation increases the local anisotropy of the momentum distributions of produced hadrons, and thus the collective flow parameters such as $v_2$ is emphasized.