Perelman's entropy for some families of canonical metrics

We numerically calculate Perelman’s entropy for a variety of canonical metrics on ${\mathbb{C}\mathbb{P}}^1$-bundles over products of Fano K"ahler-Einstein manifolds. The metrics investigated are Einstein metrics, K"ahler-Ricci solitons and quasi-Einstein metrics. The calculation of the entropy allows a rough picture of how the Ricci flow behaves on each of the manifolds in question.