Non-extensive statistical entropy, quantum groups and quantum entanglement

In this work, we explore a new connection between quantum groups and Tsallis entropy through the energy spectrum of a Hamiltonian with S U q ( 2 ) symmetry. Identifying the deformation parameter of the entropy with the parameter of deformation of the associated quantum group, we deduce Tsallis entropy for states related to such a system with S U q ( 2 ) symmetry and conducted an investigation of quantum entanglement.