  The learning rate is an information-theoretical quantity for bipartite Markov
chains describing two coupled subsystems. It is defined as the rate at which
transitions in the downstream subsystem tend to increase the mutual information
between the two subsystems, and is bounded by the dissipation arising from
these transitions. Its physical interpretation, however, is unclear, although
it has been used as a metric for the sensing performance of the downstream
subsystem. In this paper, we explore the behaviour of the learning rate for a
number of simple model systems, establishing when and how its behaviour is
distinct from the instantaneous mutual information between subsystems. In the
simplest case, the two are almost equivalent. In more complex steady-state
systems, the mutual information and the learning rate behave qualitatively
distinctly, with the learning rate clearly now reflecting the rate at which the
downstream system must update its information in response to changes in the
upstream system. It is not clear whether this quantity is the most natural
measure for sensor performance, and, indeed, we provide an example in which
optimising the learning rate over a region of parameter space of the downstream
system yields an apparently sub-optimal sensor.
