Statistical mechanics and thermodynamics for ideal fractional exclusionstatistics with mutual statistical interactions is studied systematically. Wediscuss properties of the single-state partition functions and derive thegeneral form of the cluster expansion. Assuming a certain scaling of thesingle-particle partition functions, relevant to systems of noninteractingparticles with various dispersion laws, both in a box and in an externalharmonic potential, we derive a unified form of the virial expansion. For thecase of a symmetric statistics matrix at a constant density of states, thethermodynamics is analyzed completely. We solve the microscopic problem ofmultispecies anyons in the lowest Landau level for arbitrary values of particlecharges and masses (but the same sign of charges). Based on this, we derive theequation of state which has the form implied by exclusion statistics, with thestatistics matrix coinciding with the exchange statistics matrix of anyons.Relation to one-dimensional integrable models is discussed.
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