We formulate a convenient generalization of the q-expectation value, based
on the analogy of the symmetric quantum groups and q-calculus, and show tha
t the q <-> q(-1) symmetric nonextensive entropy preserves all of the mathe
matical structure of thermodynamics just as in the case of nonsymmetric. Ts
allis statistics. Basic propreties and analogies with quantum groups are di
scussed.