Fractional exclusion statistics in general systems with interaction

I show that fractional exclusion statistics (FES) is manifested in general interacting systems and I calculate the exclusion statistics parameters. Most importantly, I show that the mutual exclusion statistics parameters–when the presence of particles in one Hilbert space influences the dimension of another Hilbert space–are proportional to the dimension of the Hilbert space on which they act. This result, although surprising and different from the usual way of understanding the FES, renders this statistics consistent and valid in the thermodynamic limit, in accordance with the conjucture introduced in J. Phys. A: Math. Theor. 40, F1013 (2007).