  A quantitative analysis of the process of condensation of bosons both in
harmonic traps and in gases is made resorting to two ingredients only: Bose
classical distribution and spectral discretness. It is shown that in order to
take properly into account statistical correlations, temperature must be
defined from first principles, based on Shannon entropy, and turns out to be
equal to $\beta^{-1}$ only for $T > T_c$ where the usual results are recovered.
Below $T_c$ a new critical temperature $T_d$ is found, where the specific heat
exhibits a sharp spike, similar to the $\lambda$-peak of superfluidity.
