Tsallis nonextensive statistics with normalized q-expectation values: thermodynamical stability and simple illustrations

We prove that the specific heat Cq/q is nonnegative for q [0,1) in the Tsallis generalized canonical ensemble with normalized q-expectation values. In this way, we show the thermodynamic stability for this ensemble. We also analyze the behavior of some thermodynamic functions such as internal energy and specific heat in the classical and quantum cases considering a spectrum of energy En= nr ( ,r>0).