I learned long ago that there are some exotic classes of statistics. One of them is called $q$-on or quon statistics. It is given by
Infinite statistics (Quantum Boltzmann statistics or Cuntz algebra) is the particular case of quon statistics with $q=0$.
Question: is there some physical model resembling $q$-statistics or quons? What is the Hamiltonian for such a thing? Is there some relativistic field theory model for that thing?