  We introduce the notion of `order-$k$ non-abelian exclusion statistics'. We
derive the associated thermodynamic equations by employing the Thermodynamic
Bethe Ansatz for specific non-diagonal scattering matrices. We make contact
with results obtained by different methods and we point out connections with
`fermionic sum formulas' for characters in a Conformal Field Theory. As an
application, we derive thermodynamic distribution functions for quasi-holes
over a class of non-abelian quantum Hall states recently proposed by Read and
Rezayi.

Statistical Mechanics;Mesoscale and Nanoscale Physics;High Energy Physics - Theory