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We derive a four-component Vlasov equation for a system composed of spin-1/2fermions (typically electrons). The orbital part of the motion is classical,whereas the spin degrees of freedom are treated in a completelyquantum-mechanical way. The corresponding hydrodynamic equations are derived bytaking velocity moments of the phase-space distribution function. Thishydrodynamic model is closed using a maximum entropy principle in the case ofthree or four constraints on the fluid moments, both for Maxwell-Boltzmann andFermi-Dirac statistics.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Semiclassical Vlasov and fluid models for an electron gas with spin effects