The Vlasov equation 
is a differential equation describing the dynamical evolution of the phase space distribution function.
The time evolution of the phase space distribution function
is governed by Liouville's theorem
which asserts that in case of dissipationless and collisionless dynamics, the phase space distribution function is constant along the trajectories of the system
Using the definition of the momentum
and Newton's law
for a force
derived from a potential
, this can be rewritten as
which is known as Vlasov equation
- ^ A. A. Vlasov (1938). "On Vibration Properties of Electron Gas" (in Russian). J. Exp. Theor. Phys. 8 (3): 291.