Any communication between systems A and B in a noisy channel maps to a model of natural selection which maximizes the rate of increase of entropy of the environment. i.e. it evolves things that look a lot like living things.

(i) axiom: if information can flow between 2 systems it will flow.

(ii) any system that allows information to flow has to be partially open (to allow information to flow (open) but to still be able to store it (some kind of boundary – i.e. closed))

(iii) partially open means A and B not isolated from the environment therefore there will always be noise in the channel between A and B.

(iv) the process of learning implies information storage and state change.

Then:

(a) Even in a purely classical environment, any action (state change in B governed by a rule) based on a message that is communicated from A to B will eventually become a different action. i.e. any rule will mutate over time due to noise.

(b) Variable inheritance of rules applied to a system in a finite environment are parameters equivalent to those in biological natural selection, where: rules = inheritance; noise = mutation; finite environment = constraint for selection to be applied.
In the simplest model of the universe consisting of bits and containing systems that are also strings of bits and where physical laws (rules) govern the state of those bits:

(a) If there are a finite number of rules and an infinite amount of time, all rules will be cycled through in interaction between any two systems and systems which result in the greatest information transfer (maximizing the rate of entropy production relative to others) and complexity (learning) will tend to increase in the systems themselves.

(b) To process and store information, such a system would need to be capable of self configuring to be a computer i.e. be Turing complete.

This is the case: a 1 dimensional (2 state, nearest neighbor) cellular automata is the simplest model of a rules based system where ‘Rule 110’ of 256 possible rules, has been proven to be Turing complete (Mathew Cook). i.e. there are systems consisting of strings of bits that are themselves computers.

So, in the simplest model of the universe, more and more complex Turing complete systems will necessarily increase over time, via ‘algorithmic’ natural selection which is a consequence of any imperfect information flow. These relatively low entropy systems need only exist at boundaries of other systems, producing waste bits which maximize the rate of increase of the overall entropy.

There are three ways in which the ‘selection’ could operate:

(1) The replication happens to subsytems of the infinitely complex, Turing complete one. Once any system stumbles upon the correct rule (one that creates something which is Turing complete), the Turing complete system keeps on growing (it’s an ecosystem) in size and complexity, at the expense of others. Although I’m not sure where the ‘waste bits’ that dump into the environment come from, this has to be an open system.

(2) The replication is separate. The Turing complete system is merely the information store (a bit like the aperiodic crystal that Schrodinger postulated) and this step has nothing to do with natural selection. A separate emergence or mechanism for replication is what creates a pool of systems on which selection can operate. Perhaps this and (1) are the same, i.e. you need a Turing machine to create emergent self-replicating sub-systems.

(3) The message transfer from A to B IS the replication, much like it is for memes.