Linear drift and entropy for regular covers

We consider a regular Riemannian cover $\text{M}$ of a compact Riemannian manifold. The linear drift $\mathrm{\ell }$ and the Kaimanovich entropy $h$ are geometric invariants defined by asymptotic properties of the Brownian motion on $\text{M}$. We show that ${\mathrm{\ell }}^2\le h$.