The thermodynamic limit for fractional exclusion statistics

I discuss Haldane's concept of generalized exclusion statistics ( 1991 Phys. Rev. Lett. 67 937) and show that it leads to inconsistencies in the calculation of the particle distribution that maximizes the partition function. These inconsistencies appear when mutual exclusion statistics is manifested between different subspecies of particles in the system. In order to eliminate these inconsistencies, I introduce new mutual exclusion statistics parameters, which are proportional to the dimension of the Hilbert subspace on which they act. These new definitions lead to properly defined particle distributions and thermodynamic properties. In another paper (Preprint 0710.0728), I show that the fractional exclusion statistic smanifested in general systems with interaction have these, physically consistent, statistics parameters.