Thermodynamics of boson and fermion systems with fractal distribution functions

TL;DR

This paper explores the thermodynamics of boson and fermion systems using fractal-inspired distribution functions, revealing connections to q-deformed Hamiltonians and comparing with ideal and quantum group symmetric gases.

Contribution

It introduces a thermodynamic analysis based on fractal distribution functions and links the generalized Bose-Einstein distribution to a q-deformed Hamiltonian.

Findings

Generalized distributions differ from ideal gases and quantum group systems.

The Bose-Einstein distribution corresponds to a q-deformed Hamiltonian.

Results highlight the thermodynamic implications of fractal and q-deformed statistics.

Abstract

Starting with the fractal inspired distribution functions for Maxwell-Boltzmann, Bose-Einstein and Fermi systems, as reported by F. B\"{u}y\"{u}kkili\c{c} and D. 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.