Non-extensive entropy in q-deformed quantum groups

On the basis of the recently proposed formalism [A. Lavagno, P.N. Swamy, Phys. Rev. E 61 (2000)], we show that the realization of the thermostatistics of q-deformed quantum groups can be built on the formalism of q-calculus. It is found that the entire structure of thermodynamics is preserved if we use an appropriate Jackson derivative instead of the ordinary thermodynamic derivative. This allows us to obtain a generalized nonextensive entropy and other thermodynamic quantities which depend on the q-basic number. The connection with nonextensive Tsallis statistics is discussed. Finally, we briefly report on applications and practical results, in particular the Bose–Einstein condensation phenomenon of q-bosons.