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We describe a mean field interacting particle system in any number ofdimensions and in a generic external potential as an ideal gas with fractionalexclusion statistics (FES). We define the FES quasiparticle energies, wecalculate the FES parameters of the system and we deduce the equations for theequilibrium particle populations. The FES gas is "ideal", in the sense that thequasiparticle energies do not depend on the other quasiparticle levelspopulations and the sum of the quasiparticle energies is equal to the totalenergy of the system. We prove that the FES formalism is equivalent to thesemi-classical or Thomas Fermi limit of the self-consistent mean-field theoryand the FES quasiparticle populations may be calculated from the Landauquasiparticle populations by making the correspondence between the FES and theLandau quasiparticle energies. The FES provides a natural semi-classical idealgas description of the interacting particle gas.

Equivalence between fractional exclusion statistics and self-consistent mean-field theory in interacting particle systems in any number of dimensions