  The generalized uncertainty relation applicable to quantum and stochastic
systems is derived within the stochastic variational method. This relation not
only reproduces the well-known inequality in quantum mechanics but also is
applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier
equation, showing that the finite minimum uncertainty between the position and
the momentum is not an inherent property of quantum mechanics but a common
feature of stochastic systems. We further discuss the possible implication of
the present study in discussing the application of the hydrodynamic picture to
microscopic systems, like relativistic heavy-ion collisions.
