Linking the theory of Maximum Entropy and Natural Selection

In the 70’s Prigogine looked for an entropy minimization principal for non-equilibrium systems - this held only for systems very slightly out of equilibrium. The opposite approach started by Edwin Thompson Jaynes in the 50s is much more promising. It attempts to unite Boltzmann’s statistical mechanics (entropy = the number of ways molecules can be arranged) with Shannon’s information theory (information entropy = number of ways bits can be arranged) to be able to apply statistical mechanics to non-equilibrium systems (as imagined by Onsager).

Jaynes extracted a principal of ‘how things happen’: all systems maximize entropy. For non equilibrium systems (i.e. where there is still energy flow) this equates to maximum RATE of entropy production.

This would rephrase the 2nd Law of Thermodynamics from its current form:

entropy tends to increase.

To:

entropy tends to increase at the maximum rate.

This still allows for local order (such as life), in environments where the overall entropy is increasing, since some ordered systems are better at creating entropy via ’structured paths’ than high entropy mess.

Since it seems that living things are supreme examples of localized order that maximizes entropy production and that all living things evolve by means of natural selection, it would be reasonable to assume that if there is a general law of maximum entropy then perhaps natural selection could be expressed in terms of physics and apply under the right circumstances to any interacting systems rather than be confined to Biology.

So how would we connect the law of maximum entropy to the law of natural selection?

Order spontaneously occurs in non-equilibrium systems, what non-equilibrium systems would operate under natural selection and what systems wouldn’t, what would the mechanisms be.

For natural selection to operate we need the following 3 conditions: systems with VARIABLE HEREDITY in a FINITE ENVIRONMENT.

[variable (mutation) heredity (a life cycle) in a finite environment (not all systems survive)].

Heredity implies information exchange between generations and since no open system is truly isolated from the rest of the universe, where other things are happening, all information exchange is subject to noise. All noise has the potential to disturb the information exchange (i.e. create variable heredity), but presumably, non-linear effects mean that the statistical likelihood of noise affecting heredity (i.e. mutation) mean that for any specific case there are noise thresholds which are significant.

The finite environment conditions are the same here as for living systems, if we imagine a section of river with a finite amount of water flowing in and out and the potential for simple whirlpools or complex systems of whirlpools with a greater flow through them, then the latter would predominate if their occurrence were possible.

The operation of noise threshold levels are the most difficult to describe and apply generally non-equilibrium systems in order to express natural selection in terms of physics.

Lets consider a whirlpool as an example of a non-equilibrium system: the structure of the whirlpool is formed by the water itself which flows through it, it is not a separate structure through which water flows (in fact perhaps all things may be like this - but that’s another story).

Each revolution of the whirlpool is like a metabolic cycle, or even a life cycle, since the molecules of water making the structure of the whirlpool are entirely replaced. If the flow of water is absolutely constant, the whirlpool will be exactly the same for the next revolution of the whirlpool.

The flow of water can never be exactly constant, however, since it sits in the real world, or rather the universe, a universe where things happen creating difference over time and therefore background noise which creates variations in the flow of water. If these variations (perturbations) are strong enough then the whirlpool will take a different shape or be destroyed.

What is the difference between a self reproducing whirlpool and something which operates under natural selection such as a self replicating molecule of DNA? A whirlpool is like a crystal, if the right conditions are there it will create order but it does not evolve because perturbations either result in it settling back to its original form or it being destroyed. Formation of whirlpools is rather like the creation of a life form from scratch, but one which cannot change or evolve. DNA as Schrodinger predicted is much more like an aperiodic crystal, one where there are a very large number of possible different states and therefore capable of storing a large amount of information. (NB don’t fall into the entropy paradox: life forms = highly ordered = low entropy vs life forms = complex = large number of states = high entropy. There is no paradox since although complex systems are higher entropy than simple systems they are lower entropy than mess - in fact, to rephrase Arthur C. Clark (Any sufficiently advanced technology is indistinguishable from magic) Any sufficiently advanced technology is indistinguishable from junk).

For the whirlpool model to behave like a system under natural selection, it would would have to somehow reconfigure under perturbation to a more complex system with increased flow of water.

How does DNA fit into this model. DNA is an information store, a recipe for building complicated non-equilibrium systems. A whirlpool has no stored recipe, but the conditions that create it from scratch happen often enough that it forms. One piece of DNA may be rather like another in terms of entropy, but the resulting organisms they produce may differ greatly in terms of complexity. Is an intermediate recipe store necessary for evolution by natural selection.

But surely, DNA itself operates under natural selection, some strands are longer and more complex than others, the recipe itself has structure and so the 3 tier system above cannot explain the difference between naturally selected systems and non evolving ones?

[ Notes: at this point I am stuck!]