  Recent experiments have indicated that many biological systems self-organise
near their critical point, which hints at a common design principle. While it
has been suggested that information transmission is optimized near the critical
point, it remains unclear how information transmission depends on the dynamics
of the input signal, the distance over which the information needs to be
transmitted, and the distance to the critical point. Here we employ stochastic
simulations of a driven 2D Ising system and study the instantaneous mutual
information and the information transmission rate between a driven input spin
and an output spin. The instantaneous mutual information varies
non-monotonically with the temperature, but increases monotonically with the
correlation time of the input signal. In contrast, the information transmission
rate exhibits a maximum as a function of the input correlation time. Moreover,
there exists an optimal temperature that maximizes this maximum information
transmission rate. It arises from a tradeoff between the necessity to respond
fast to changes in the input so that more information per unit amount of time
can be transmitted, and the need to respond to reliably. The optimal
temperature lies above the critical point, but moves towards it as the distance
between the input and output spin is increased.
