  Herein, in the context of third version of nonextensive statistical
mechanics, theory generalizing the Boltzmann-Gibbs-Shannon statistics, we
displayed 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= H_A+ H_B;
specifically, the calculation of the internal energy in the full Hilbert space
is different from the calculation done in the Hilbert subspaces, in other
words, U_tot is different to U_A +U_B. We carry out analytical calculations
(for 2 spins 1/2). The results exactly indicate that the alternative method of
matrices E_A and E_B is suitable for the calculations of the internal energy,
therefore, the matrix that contains the physical information of the system is
the matrix rho^q but not \rho.
