Multivariate Normal Entropy
Result
Suppose $x: \Omega \to \R ^d$ has normal
density $g: \R ^d \to \R $ on probability space
$(\Omega , \mathcal{A} , \mathbfsf{P} )$.
Suppose $x$ has mean $\mu \in \R ^d$ and
covariance $\Sigma \succ 0$.
Then the entropy of $x$ is
\[ h(g) = -\int g \log g = \frac{1}{2} \log ((2\pi e)^d \det \Sigma ) \]
This result tells us the multivariate normal entropy (or Gaussian entropy).