This post contains some math and physics that I need frequently but don’t know by heart.
Continuous random variable $X$ with pdf $p$ has expectation \(\underset{x\sim p(X)}{\mathbb{E}}\left[x\right]=\int x\cdot p(x)\mathrm{d}x.\)The Kullback-Leibler divergence can be interpreted as an expectation value as well \(\mathsf{KL}(p\vert\vert q)=\int p(x)\log\frac{p(x)}{q(x)}\mathrm{d}x.\)Some of its properties include asymmetry $\mathsf{KL}(p\vert\vert q)\ne\mathsf{KL}(q\vert\vert p),$ non-negativity $\mathsf{KL}(p\vert\vert q)\ge 0,$ and $\mathsf{KL}(p\vert\vert q)=0\iff p(x)=q(x)~\forall x.$