Non-extensive entropy in q-deformed quantum groups

On the basis of the recently proposed formalism [A. Lavagno, P.N. Swamy, Ph ys. 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 an d other thermodynamic quantities which depend on the q-basic number. The co nnection with nonextensive Tsallis statistics is discussed. Finally, we bri efly report on applications and practical results, in particular the Bose-E instein condensation phenomenon of q-bosons. (C) 2001 Elsevier Science Ltd. All rights reserved.