q-Deformed structures and nonextensive statistics: a comparative study

The thermostatistics of q-deformed bosons and fermions can be built on the formalism of q-calculus. As in nonextensive statistics, the entire structure of thermodynamics is preserved but there are crucial differences between the two theories. We derive the most important thermodynamic functions of q-deformed fermions and bosons. We also study the semiclassical limit and the low-temperature behavior and point out the similarities and differences with the results of nonextensive statistics.