  In this note, we generalize the notion of entropy for potentials in a
relative full Monge-Amp\`ere mass $\mathcal{E}(X, \theta, \phi)$, for a model
potential $\phi$. We then investigate stability properties of this condition
with respect to blow-ups and perturbation of the cohomology class. We also
prove a Moser-Trudinger type inequality with general weight and we show that
functions with finite entropy lie in a relative energy class
$\mathcal{E}^{\frac{n}{n-1}}(X, \theta, \phi)$ (provided $n>1$), while they
have the same singularities of $\phi$ when $n=1$.
