Let $P$ be a transition matrix of a random walk in an undirected regular graph $G$. Let $\pi$ be a distribution on $V(G)$. The Shannon entropy of $\pi$ is defined by
$H(\pi)=-\sum_{v \in V(G)}\pi_v\cdot\log(\pi_v).$
How do we prove that $H(P\pi)\ge H(\pi)$ ?