arXiv:2611.13040v1 Announce Type: cross Abstract: In this paper, we establish the concavity of R\'enyi entropy and R\'enyi entropy power along heat flow on Euclidean space of arbitrary dimension, for R\'enyi orders $\alpha\in[1,2]$. More generally, we prove the corresponding result along the heat flow generated by the Witten Laplacian on complete Riemannian manifolds under a suitable curvature-dimension condition. Our argument builds on novel functional inequalities that were recently developed for the study of Tsallis entropy concavity along the heat flow. We extend both these inequalities and the resulting concavity theorem from the Euclidean setting to the Riemannian manifold setting. In addition, we establish the complete monotonicity of Tsallis entropy of order $2$ along the heat flow and derive its spectral decomposition.