A derivation of Liouville's equation is given using the formalism employed by Hopf (1952) and Edwards (1964) in their derivation of the equations governing, respectively, the characteristic-density functional and probability-density functional associated with turbulent fluids.

This content is only available via PDF.
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.