The Vlasov equation [1] 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.

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

(1) |

(2) |

References:

- [1]^ A. A. Vlasov (1938). "On Vibration Properties of Electron Gas" (in Russian). J. Exp. Theor. Phys. 8 (3): 291.

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