  Motivated by the classical De Bruijn's identity for the additive Gaussian
noise channel, in this paper we consider a generalized setting where the
channel is modelled via stochastic differential equations driven by fractional
Brownian motion with Hurst parameter $H\in(0,1)$. We derive generalized De
Bruijn's identity for Shannon entropy and Kullback-Leibler divergence by means
of It\^o's formula, and present two applications. In the first application we
demonstrate its equivalence with Stein's identity for Gaussian distributions,
while in the second application, we show that for $H \in (0,1/2]$, the entropy
power is concave in time while for $H \in (1/2,1)$ it is convex in time when
the initial distribution is Gaussian. Compared with the classical case of $H =
1/2$, the time parameter plays an interesting and significant role in the
analysis of these quantities.
