  We establish a connection between the relative Classical entropy and the
relative Fermi-Dirac entropy, allowing to transpose, in the context of the
Boltzmann or Landau equation, any entropy-entropy production inequality from
one case to the other; therefore providing entropy-entropy production
inequalities for the Boltzmann-Fermi-Dirac operator, similar to the ones of the
Classical Boltzmann operator. We also provide a generalized version of the
Csisz{\'a}r-Kullback-Pinsker inequality to weighted Lp norms, 1 $\le$ p $\le$ 2
and a wide class of entropies.
