While looking around for material on Illya Prigogine's attempt to reconcile dynamics and thermodynamics so as to see where his views currently stand, I inadvertently ran across an article which may be of some interest. It is entitled "Thermodynamics, Evolution, and Behavior." Written by Rod Swenson for "The Encyclopedia of Comparative Psychology," it is non-technical and highly accessible. Moreover, looking over it, the article appears to be largely on target - although I believe the author overstates his case. His article may be largely be seen as a history of ideas in the area.

His central argument (minus the frills) appears to be:

1. Darwinian evolution with its reliance upon reproduction and natural selection can only be applied internally to the biosphere, not to the biosphere itself.

2. Evolution is best understood in a sense which is broader than "Darwinian evolution" such that it may be extended to include the biosphere as a whole.

3. Darwinian evolution presupposes a world in which every organism is "striving its utmost to increase, there is therefore the strongest possible power tending to make each site support as much life as possible."

4. However, if one is to explain this "fecundity principle" (3), one must look elsewhere.

5. Given a potential which exceeds a certain threshold, in accordance with the second law, energy flow will not simply tend to occur, but it will tend to be maximized - both within and outside of the biological realm.

6. Ordered systems are more efficient than disordered systems in maximising energy flow.

7. Self-organisation will tend to occur as a natural consequence of the tendency of physical systems to maximise energy flow.

8. Among the set of paths which lead to entropy production, systems will naturally tend to select the path which maximised entropy production, consequently maximising energy flow by prefering the ordered flow of energy which has as a consequence the self-organisation of systems in order to maximise the flow of energy.

9. As such, rather than being either a violation of the second law of thermodynamics or the result of an extremely improbable event which is permitted by the law so long as it is paid for, life is a natural process which, when given the right conditions is highly probable, as such, it is no accident that life originated soon after it became possible in the history of our planet.

Thermodynamics, Evolution, and Behavior

Rod Swenson

From The Encyclopedia of Comparative Psychology, G. Greenberg and M. Haraway (Eds.), New York: Garland Publishers, Inc. 1997

http://www.entropylaw.com/thermoevolution1.html

The point which seems most problematic (in my view) is his overstatement of the case for the "Principle of Maximum Entropy Production."

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Another somewhat more technical article which deals with the "Principle of Maximum Entropy Production" is the following:

Maximisation Principles and Daisyworld

G.J. Ackland

Dated: September 15, 2006

http://arxiv.org/pdf/cond-mat/0307567

This author argues against the universality of the "Principle of Maximum Entropy Production" even in far from equilibrium regimes.

Nevertheless, the "Principle of Maximum Entropy Production" is widely used by systems theorists and often appealed to (in one form or another) in explaining the behaviour of self-organising systems - Bernard cells, etc. The first article mentions a number of different examples of such systems, although my favourite is conspicuously absent: lightning discharges - which self-organise to carve paths of least resistance through the atmosphere, leading to the rapid reduction of electric potentials.

As one indication of the significance which is attached to maximum entropy production, I would suggest the following:

Oral Programme - NP5 Dynamic reconstruction from time series data / Maximum entropy production

EGS-AGU-EUG Joint Assembly

Nice, France, 11 Apr 2003

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In Sum

It would seem that in systems which are sufficiently distant from equilibrium, there exists a tendency for systems to evolve over time in such a way that they maximise entropy production and energy flow through the generation of ordered energy flows which are more efficient than disordered flows in transfering energy. The generation of ordered energy flows generally involves a process of symmetry-breaking and self-organisation which fascilitates these flows and roughly corresponds to Darwin's fecundity principle whereby living organisms strive to make "each site support as much life as possible." Moreover, the widespread existence such self-organisation even in non-biological realms would seem to make the life appear less like some sort of cosmic accident than as a natural, almost to-be-expected occurence.

In addition, it underscores the point that neither the existence of life nor its evolution are to be seen as violating the second law, but as agents of the second law which fascilitate the production of entropy by maximising energy flow that are able to benefit as a result of their acting in this capacity. Nevertheless, the tendency of systems to maximise entropy production is just that: a tendency - not a law, although it is a principle through which we are often able to understand even non-biological systems and their tendency to spontaneously self-organise. Moreover, it would make sense if it were merely a tendency - insofar as self-organisation is in all likelihood itself a form of stochastic process whereby fluctuations are successively amplified to increasingly larger scales in a probablistic fashion - which would also explain the sensitivity of such systems to their environment. (I mentioned a paper that touched on this last point some time ago in relation to the Brusselator, I believe - which is one of many chemical oscillators, or "clocks.")

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As for the results of my search on Illya Prigogine, I found that his programme is one of several, but certainly alive and well - with work being done at the University of Texas, in Beligium, the former Soviet Union and Singapore.

Here are some of the more recent technical papers - for those who might stand a better than I of making heads or tails of them...

Hamiltonian dynamics, nanosystems, and nonequilibrium statistical mechanics

Pierre Gaspard

Lecture notes for the International Summer School

Fundamental Problems in Statistical Physics XI

(Leuven, Belgium, September 4-17, 2005)

http://arxiv.org/pdf/cond-mat/0603382

Generalized Quantum Dynamics with Arrow of Time

Vadim V. Asadov and Oleg V. Kechkin

13 Dec 2006

http://arxiv.org/pdf/hep-th/0612122

Parity Violation and Arrow of Time in Generalized Quantum Dynamics

Vadim V. Asadov and Oleg V. Kechkin

13 Dec 2006

http://arxiv.org/pdf/hep-th/0612123

Gravity as Classical Effect in Generalized Relativistic Quantum Mechanics on Flat Background

Vadim V. Asadov and Oleg V. Kechkin

15 Dec 2006

http://arxiv.org/pdf/hep-th/0612162

Time evolution of the relativistic unstable electromagnetic system in the unified formulation of quantum and kinetic dynamics

S.Eh.Shirmovsky

22 June 2006

http://arxiv.org/pdf/quant-ph/0512115

Arrow of time in generalized quantum theory and its classical limit dynamics

21 Aug 2006

Vadim V. Asadov and Oleg V. Kechkin

http://arxiv.org/pdf/hep-th/0608148