The $H_{infty}$ entropy in $H_{infty}$ control theory is discussed based on investigating information transmission in continuous-time linear stochastic systems. It is proved that the stabilizing feedback does not change the time-average information transmission between system input and output, and the $H_{infty}$ entropies of open- and closed-loop stable transfer functions are bounded by mutual information rate between input and output in the open-loop system. Furthermore, a new $H_2$ upper bound for $H_{infty}$ entropy is introduced with a numerical example. Thus the $H_{infty}$ entropy of a stable transfer function is sandwiched between $H_2$ norms of the original system and a static feedback system.