  We consider two statistically independent systems described by the same
entropy belonging to the two-parameter family of Sharma-Mittal. Assuming a weak
interaction among the systems, allowing in this way an exchange of heat and
work, we analyze, both in the entropy representation and in the energy
representation, the evolution toward the equilibrium. The thermodynamics
evolution is controlled by two scalar quantities identified with the
temperature and the pressure of the system. The thermodynamical stability
conditions of the equilibrium state are analyzed in both representations. Their
relationship with the concavity conditions for the entropy and with the
convexity conditions for the energy are spotlighted.
