  We develop a model based on the fractional exclusion statistics (FES)
applicable to non-homogeneous interacting particle systems. Here the species
represent elementary volumes in an (s+1)-dimensional space, formed by the
direct product between the s-dimensional space of positions and the
quasiparticle energy axis. The model is particularly suitable for systems with
localized states. We prove the feasibility of our method by applying it to
systems of different degrees of complexities. We first apply the formalism on
simpler systems, formed of two sub-systems, and present numerical and
analytical thermodynamic calculations, pointing out the quasiparticle
population inversion and maxima in the heat capacity, in contrast to systems
with 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, we
consider systems with several degrees of disorder, which are prototypical for
models with glassy behavior. We find that the disorder produces a spatial
segregation of quasiparticles at low energies which significantly affects the
heat capacity and the entropy of the system.
