Iterated Entropy Derivatives and Binary Entropy Inequalities

Tanay Wakhare

We embark on a systematic study of the $(k+1)$-th derivative of $x^{k-r}H(x^r)$, where $H(x):=-x\log x-(1-x)\log (1-x)$ is the binary entropy and $k>r\ge 1$ are integers. Our motiv…