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

We describe a mean field interacting particle system in any number of dimensions and in a generic external potential as an ideal gas with fractional exclusion statistics (FES). We define the FES quasiparticle energies, we calculate the FES parameters of the system and we deduce the equations for the equilibrium particle populations. The FES gas is "ideal", in the sense that the quasiparticle energies do not depend on the other quasiparticle levels populations and the sum of the quasiparticle energies is equal to the total energy of the system. We prove that the FES formalism is equivalent to the semi-classical or Thomas Fermi limit of the self-consistent mean-field theory and the FES quasiparticle populations may be calculated from the Landau quasiparticle populations by making the correspondence between the FES and the Landau quasiparticle energies. The FES provides a natural semi-classical ideal gas description of the interacting particle gas.