  We compute the Minimal Entropy of every closed, orientable $3$-manifold,
showing that its cube equals the sum of the cubes of the minimal entropies of
each hyperbolic component arising from the $JSJ$ decomposition of each prime
summand. As a consequence we show that the cube of the Minimal Entropy is
additive with respect to both the prime and the $JSJ$ decomposition, thus
concluding that for closed orientable $3$-manifolds the cube of the Minimal
Entropy is proportional to the simplicity volume. This answers a conjecture
asked by Anderson and Paternain for irreducible manifolds.
