mutual information

The KL divergence between the joint and the marginals. For joint distribution $P_{X\times Y}$ with marginals $P_X$ and $P_Y$, the mutual information is $I(X;Y)=D_{\text{KL}}(P_{X,Y}\Vert P_X\otimes P_Y)$.

The mutual information is a measure of dependence between $X$ and $Y$: If you know one, how much do you know about the other? (The MI is symmetric). $I(X;Y)=0$ iff $X$ and $Y$ are independent.