Extensivity of Rényi entropy for the Laplace–de Finetti distribution

• de Finetti distributions have extensive Rényi entropy.
• Lower and upper bounds for Boltzmann–Gibbs entropy for de Finetti distributions.
• Lower and upper bounds for Rényi entropy for de Finetti distributions.

The Boltzmann–Gibbs entropy is known to be asymptotically extensive for the Laplace–de Finetti distribution. We prove here that the same result holds in the case of the Rényi entropy. We also show some interesting lower and upper bounds for the asymptotic limit of these entropies.