Classical probability waves

Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, described by the probability density and the generating function of the Hamilton-Jacobi theory. It is shown that by introducing a minimum distance in the coordinate space, the action distributions aquire the phase-space dispersion specific to the quantum objects. At finite temperature, probability density waves propagating with the sound velocity can arise as nonstationary solutions of the classical Fokker-Planck equation. The results suggest that in a system of quantum Brownian particles, a transition from complex to real probability waves could be observed.