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