  We outline formal and physical similarities between the quantum dynamics of
open systems, and the mesoscopic description of classical systems affected by
weak noise. The main tool of our interest is the dissipative Wigner equation,
that, for suitable timescales, becomes analogous to the Fokker-Planck equation
describing classical advection and diffusion. This correspondence allows in
principle to surmise a finite resolution, other than the Planck scale, for the
quantized state space of the open system, particularly meaningful when the
latter underlies chaotic classical dynamics. We provide representative examples
of the quantum-stochastic parallel with noisy Hopf cycles and Van der Pol type
oscillators.

Quantum Physics;Chaotic Dynamics