Actually I would disagree with Nick or Ami. Although I am not familiar with the chain rules of entropy, we can use a simple counter example. Suppose $X\sim N(0,\sigma^2)\in \mathbb{R}$. Then its entropy is given by (derivation given here) $$ H=\frac{1}{2}\log(2\pi)+\log(\sigma)+\frac{1}{2} $$ The entropy is dependent on $\sigma$, which can be modified by scaling. e.g. $Y=2X$ implies $\sigma_Y=2\sigma_X$, which yields $H(Y)-H(X)=\log 2\neq 0$
Ruobin Han
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