What's the tradeoff between "delete all state in the world with 100% certainty" and "be able to choose any next state of the world with (100-epsilon)% certainty"?
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