I think looking into ergodic theory would help fill in the gap between completely random and completely rule based. In ergodic theory you have some kind of 'state' and a function way to 'advance' the state, if you partition the state space you also get a sequence of 'bytes' to send (simple example: take a number in [0,1] multiply by 10, send the first digit and continue with the remainder). The state needs a distribution, that needs to be preserved by advancing the state, but it's pretty close to running an algorithm otherwise.

You'll probably also want to look at uniquely ergodic systems. Those are interesting in the way that they behave 'random' for every input, one example is if you keep multiplying a number by anything other than a power of 10 and divide it by a power of 10 so it's between 0 and 1. Turns out you get the same distribution of results every time (eventually).

And while you can define an entropy rate without I think ergodic theory also helps inform why that is the correct generalisation. Your current article only considers the case where each digit is independently random (it's clear why, it's a lot simpler and all that information theory tends to talk about).