  We provide the notion of entropy for a classical Klein-Gordon real wave, that
we derive as particular case of a notion entropy for a vector in a Hilbert
space with respect to a real linear subspace. We then consider a localised
automorphism on the Rindler spacetime, in the context of a free neutral Quantum
Field Theory, that is associated with a second quantised wave, and we
explicitly compute its entropy $S$, that turns out to be given by the entropy
of the associated classical wave. Here $S$ is defined as the relative entropy
between the Rindler vacuum state and the corresponding sector state (coherent
state). By $\lambda$-translating the Rindler spacetime into itself along the
upper null horizon, we study the behaviour of the corresponding entropy
$S(\lambda)$. In particular, we show that the QNEC inequality in the form
$\frac{d^2}{d\lambda^2}S(\lambda)\geq 0$ holds true for coherent states,
because $\frac{d^2}{d\lambda^2}S(\lambda)$ is the integral along the space
horizon of a manifestly non-negative quantity, the component of the
stress-energy tensor in the null upper horizon direction.
