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We develop a model based on the fractional exclusion statistics (FES)applicable to non-homogeneous interacting particle systems. Here the speciesrepresent elementary volumes in an (s+1)-dimensional space, formed by thedirect product between the s-dimensional space of positions and thequasiparticle energy axis. The model is particularly suitable for systems withlocalized states. We prove the feasibility of our method by applying it tosystems of different degrees of complexities. We first apply the formalism onsimpler systems, formed of two sub-systems, and present numerical andanalytical thermodynamic calculations, pointing out the quasiparticlepopulation inversion and maxima in the heat capacity, in contrast to systemswith only diagonal (direct) FES parameters. Further we investigate larger,non-homogeneous systems with repulsive screened Coulomb interactions,indicating accumulation and depletion effects at the interfaces. Finally, weconsider systems with several degrees of disorder, which are prototypical formodels with glassy behavior. We find that the disorder produces a spatialsegregation of quasiparticles at low energies which significantly affects theheat capacity and the entropy of the system.

Fractional exclusion statistics in disordered interacting particle systems