We discuss some relevant properties within the framework of a recently
proposed generalized Boltzmann-Gibbs statistics. We then apply this f
ormalism to calculate the thermal dependence of the specific heat asso
ciated with a free particle (epsilon(n) = An2 + B; A > 0). In addition
to that, we calculate the classical limit for a larger family of syst
ems (epsilon(n) = An(r) + B; A, r > 0).