Let's say $X$ and $Y$ are two random variables. Is there a general form for the entropy of $P(X+Y)$ where $Y \sim N(0, \sigma) $ and independent from $X$? $P$ is the pdf of the random variable $X+Y$. $X$ can be any random variable.

Let's say $X$ and $Y$ are two random variables where $Y \sim N(0, \sigma) $ and independent from $X$. Is there a general way to express the entropy $H(X+Y)$ in terms $H(X)$? $X$ can be any random variable.

Entropy of $P(X+Y)$ where $Y \sim N(0, \sigma) $ and independent from X?

Let's say $X$ and $Y$ are two random variables. Is there a general form for the entropy of $P(X+Y)$ where $Y \sim N(0, \sigma) $ and independent from $X$? $P$ is the pdf of the random variable $X+Y$. $X$ can be any random variable.