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##### Variational formulation of the Vlasov equation

**Authors**: J. da ProvidĂȘncia and C. Fiolhais

**Ref.**: Journal of Physics A **20**, 3877-3886 (1987)

**Abstract**: A new variational framework for the Liouville equation is presented. The Vlasov equation is obtained from the complete factorisation of the trial distribution function, while the linearised Vlasov equation arises from the additional assumption of small oscillations around an equilibrium state. Is is stressed that the definition of this state does not necessarily require minimisation of the free energy. The classical energy-weighted sum rule is derived.