Solution to a problem found by calculating the magnetic internal energy inside nonextensive statistical mechanics

Herein, in the context of third version of nonextensive statistical mechanics, a theory that generalizes the Boltzmann-Gibbs-Shannon's statistics, we display a solution for an anomaly found by calculating the internal energy for a composite A + B, of 2 spines 1/2, with additive Hamiltonian H = HA + HB. Specifically, the calculations of the internal energy in the full Hilbert space is different from the calculations done in the Hilbert subspaces, in other words, Utotal is different to UA + UB. We carry out analytical calculations. The results exactly indicate that the alternative method of matrices EA and EB is suitable for the calculations of the internal energy. Consequently, the matrix that holds the physical information of the system is ρq. © Electronic Journal of Theoretical Physics.