Thermodynamics of boson and fermion systems with fractal distribution functions.

Starting with the fractal-inspired distribution functions for Maxwell-Boltzmann, Bose-Einstein, and Fermi systems, as reported by Büyükkiliç and Demirhan, we obtain the corresponding probability distributions and study their thermodynamic behavior. We compare our results with those corresponding to ideal gases (q=1) and Bose-Einstein and Fermi systems with quantum group symmetry. In particular, we show that the Hamiltonian that gives the Bose-Einstein generalized distribution function can be interpreted as a q deformation of the ideal gas Hamiltonian.