  We study the relative entropy, in the sense of Araki, for the representation
of a self-dual CAR algebra $\mathfrak{A}_{SDC}(\mathcal{H},\Gamma)$. We notice,
for a specific choice of $f \in \mathcal{H}$, that the associated element in
$\mathfrak{A}_{SDC}(\mathcal{H},\Gamma)$ is unitary. As a consequence, we
explicitly compute the relative entropy between a quasifree state over
$\mathfrak{A}_{SDC}(\mathcal{H},\Gamma)$ and an excitation of it with respect
to the abovely mentioned unitary element. The generality of the approach,
allows us to consider $\mathcal{H}$ as the Hilbert space of solutions of the
classical Dirac equation over globally hyperbolic spacetimes, making our
result, a computation of relative entropy for a Fermionic Quantum Field Theory.
Our result extends those of Longo and Casini et al. for the relative entropy
between a quasifree state and a coherent excitation for a free Scalar Quantum
Field Theory, to the case of fermions. As a first application, we computed such
a relative entropy for a Majorana field on an ultrastatic spacetime.
