[TomAnthony]

In Information Theory, there is a concept of Channel Capacity. If a channel is defined as the probability of the output being s if you send a, across all possible values of a, then the Channel Capacity is the maximum amount of information you can communicate across this channel, measured in bits.

To achieve the Channel Capacity you need to find the optimum distribution across a - i.e. what set of signals maximises the information you can transmit on this channel. There are known algorithms for finding this distribution (e.g. Blahut-Arimoto).

Now if you model the world as a channel, where s represents the reachable states and a represents the actions the agent can take (and the channel, P(s|a), represents the dynamics of the world), you can calculate what actions allow you maximal control (in terms of states you can controllably reach).

More info in this paper: https://uhra.herts.ac.uk/handle/2299/15376