Definition (Differential cross-entropy)

$X\sim f_{X},Y\sim f_{Y}$ with $S_{X}\subset S_{Y}\subset \mathbb{R}$, the differential cross-entropy between $f_{X}$ and $f_{Y}$ is $$h(f_{X};f_{Y})=\int_{S_{X}}f_{X}(t)\log_{2} \frac{1}{f_{Y}(t)}dt$$