  Assuming that the free energy of a gas depends non-locally on the logarithm
of its mass density, the body force in the resulting equation of motion
consists of the sum of density gradient terms. Truncating this series after the
second term, Bohm's quantum potential and the Madelung equation are identically
obtained, showing explicitly that some of the hypotheses that led to the
formulation of quantum mechanics admit a classical interpretation based on
non-locality.
