Open Systems and Evolution

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Open Systems and Evolution

Postby Timothy Chase » Mon Mar 26, 2007 1:02 am

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."

*

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


*

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.")

*

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
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Postby Timothy Chase » Mon Mar 26, 2007 3:53 am

PS

I figured I owed something like the above to those who expressed interest in the "open system response" to the "thermodynamic argument for the impossibility of evolution" which is often made by creationists. It takes the response a few steps further than simply saying that, "The second law does not forbid evolution since the biosphere is an open system," arguing not in terms of what is merely possible but perhaps highly improbable, but in terms of that which can be understood as a natural and perhaps likely occurence - given the appropriate conditions.

Additionally, looking up one of the authors from the 2003 conference in Nice, France, I was able to find a paper devoted to the principle of "maximised entropy production":

Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
Roderick Dewar
Submitted to J. Phys. A. : 7 March 2002
Revised version accepted : 4 December 2002
http://arxiv.org/abs/cond-mat/0005382v1


Interestingly, it explicitly touches on the ideas of both Jaynes and Prigogine. (I knew nothing of Jaynes until a couple of weeks ago, but was deeply interested in the ideas of Illya Prigogine more than twenty years ago.) However, I have as of yet to read the whole thing...

Wish me luck!

:shock:
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Postby Timothy Chase » Mon Mar 26, 2007 7:20 am

Good grief!

This is beginning to look like another one of those great landmasses I had no idea was there....

Oh well, time to go to bed.
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Postby Timothy Chase » Mon Mar 26, 2007 4:41 pm

For those who are interested, Stijn Bruers surveys various MinMax entropy production principles and the domains of their applicability in a recent paper entitled "Classification and discussion of macroscopic entropy production principles." Interestingly, he also discusses the limitations of proofs by Roderick Dewars (see above) in an appendix - where the explanation, in far from equilibrium instances of criticality, appears to revolve around the existence of Markov chains, or alternatively, stochastic processes.

Stijn Bruers wrote:Appendix: Comments on Dewars proofs

The important articles by Dewar [16, 17] are often cited as theoretical proofs of the MaxEP principle. However, his proofs are not yet complete, especially considering the far-from-equilibrium principles. This should not be strange, because we already showed that these principles are not always valid, and the actual search is for correct criteria for their validities. Here we will briefly present a simple double spin-chain model in order to better understand the proofs by Dewar and its shortcomings. We will try to use the notation of [16, 17] as much as possible...

Classification and discussion of macroscopic entropy production principles
Stijn Bruers
5 Sep 2006
http://arxiv.org/pdf/cond-mat/0604482
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Postby Timothy Chase » Tue Mar 27, 2007 4:34 pm

An outline of the correct argument regarding self-organisation within an open system...

1. Second law of thermodynamics - the entropy within a system never decreases
2. Free energy exists in systems which are in a state of non-equilibrium according to well-known principles which can be mathematically expressed*
3. Systems tend towards a state of maximum entropy production
4. Maximum entropy production implies the least dissipation of energy - within any given system and subject to the constraints of that system, energy will tend to be transported in the most efficient means possible
5. Organised energy flows are more efficient than disorganised energy flows
6. Within systems which are distant from thermodynamic equilibrium and under whatever constraints exist within a given system, matter will tend to undergo a process of self-organisation which facilitates organised energy flows

Instances of self-organisation are widespread, including areas as diverse as lightning, Bernard cells, chemical oscillators, climate systems, biological systems, ecological systems, evolution and economics. For example, life has a tendency to grow so as to make use of all available energy, and in the process fascilitate the most efficient energy transfer possible. Likewise, a process of self-organisation which leads to the origin of life would be an instance of self-organisation resulting in organised energy flows.

* For example, if e = the energy of sunlight as thermal radiation, t1 = the temperature associated with this radiation, t2 = the temperature of the earth, then the free energy which is capable of performing work is given as:

e(t1-t2)/t1



PS

I guess thermodynamics may have to give up the title of "the dismal science" - given the "six steps of self-organisation" listed above...
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Postby Timothy Chase » Wed Mar 28, 2007 5:20 am

My apologies. :oops:

I finally had a chance to look over the article by Stijn Bruers.

Judging from what he wrote, the various principles regarding entropy production (particularly in far from equilibrium conditions) are not rquite ready for prime time. This would include the work of Dewars. They are suggestive - at least in the sense of what is currently being thought "reasonable" in the field - but beyond certain narrowly defined contexts, I believe that is all that can be fairly said.

In any case, something to look into as time permits.
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Postby tubataxidriver » Wed Mar 28, 2007 1:55 pm

Keep going, Tim. This makes very interesting reading (at least for me), and reminds me why I dropped thermodynamics and focused on quantum matters as soon as I could. The issue of scaling thermodynamics up from the quantum arena, through chemistry up to the macroscopic / ecological arena is a challenging one. We have a dire need of a "Brief History of Time" treatment of this important topic. Is there such a book?

Jeremy Hodge
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Open Systems and Evolution

Postby Timothy Chase » Wed Mar 28, 2007 5:17 pm

On 28/03/07, tubataxidriver wrote:
Keep going, Tim. This makes very interesting reading (at least for me), and
reminds me why I dropped thermodynamics and focused on quantum matters as
soon as I could. The issue of scaling thermodynamics up from the quantum
arena, through chemistry up to the macroscopic / ecological arena is a
challenging one. We have a dire need of a "Brief History of Time" treatment
of this important topic. Is there such a book?

Jeremy Hodge

The books which I had back in the early eighties were "Order Out of
Chaos" and "From Being to Becoming." Both by Illya Prigogine.
"Order" is specifically meant for a wide audience. "From Being..." is
semi-tech. I looked at the equations - and they were clearly
unfinished.

At a technical level, Illya Prigogine was working on a formalism
involving superoperators. To get at what those are, it is best to
begin with a function. A function takes as an input a number and
gives as an output another number. An operator is somewhat higher
level, taking a function as an input and giving another function as an
output. Then in the case of the superoperator, the input and outputs
are themselves operators. Interesting approach, but most certainly
incomplete.

In any case, what Dewars is working on is a different approach
altogether, something which he views as an outgrowth of Jaynes'
approach to entropy. In the case of Jaynes' approach, so to deal with
it, one should first look at Jaynes.

In Jaynes' approach, entropy would in essence be the logarithm of the
volume in phase space for a given macrostate, e.g., where the
macrostate consists of a unique state, such as my cup of coffee at a
specific temperature and position. The volume in phase space would
consist of a count of the microstates which the macrostate is
equivilent to - where each microstate for the cup of coffee would be
each unique state for all of the particles within the coffee
considered as a whole - where each particle is regarded in terms of
its position and momentum. In this way, it is what is taken to be the
entropy according to standard statistical mechanics. However, he
draws upon the "entropy" of information theory as a means of
justifying the entropy of statistical mechanics - which is in essence
the defining characteristic of his approach to entropy. One of
several "mainstream" approaches - which essentially reduce to how we
interpret the physical theories rather than how well they describe the
systems to which they are applied.

Dewar is taking a Jaynesian approach to entropy, but attempting to
apply it within the context of dynamic, non-equilibrium systems - by
applying the entropy of information theory not to stationary "states"
but to dynamic "paths." There would be the path at the macrolevel of
description, then all of the paths at the microlevel which the path at
the macrolevel is equivilent to. As such, under equilibrium
conditions, the macrolevel path would reduce to the macrostate - at
which point presumably one could replace the paths at the microlevel
with the microstates of the standard equilibrium formulation.

However, even at this point, the approach isn't making sense to me.
For one thing, the dimensionality of paths would be different from
those of states. Likewise, the replacement of the individual paths at
the microlevel with corresponding states would seem to require some
sort of justification if one actually wishes to argue that it reduces
to the Jaynesian approach under equilibrium conditions. Then there is
the question of dimensionality: volume in phase space in standard
statistical mechanics is action to the power of 3N where N is the
number of particles (at least when one considers three dimensions -
and where action is distance times momentum), whereas the volume
of paths would clearly be different.

But these are my own criticisms. Presumably physical dimensionality
wouldn't really be an issue if the Jaynesian approach itself is valid.

Then there is the whole problem of it being particularly vague.
Bristling with mathematics, no doubt, but how exactly one would apply
the mathematics to a given physical system seems especially
problematic. The critique which I pointed out deals with the
mathematics and applications to various physical systems. It is
possible that what we are speaking of by the maximisation of entropy
for a given stationary non-equilibrium state would be local optima -
this might make sense. But... Dewars is perhaps the best that they
have to offer at this point - at least in far from equilibrium
conditions.

I am of the view that the field is decidedly immature. The critique,
however, would be a good overview at a technical level of the concepts
and principles (or causal generalisations) they are working with, as
well as some of the physical systems which such principles should be
tested against. Is there a sense in which entropy production is
maximised within non-equilibrium systems? Perhaps. Perhaps not. Or
perhaps the systems to which they would apply the sort of principles
they are looking for simply cannot be grasped it that way. A general
principle of the form that they are looking for may simply be too
abstract to be generally applicable to all physical systems.

Anyway, jumped the gun. Shouldn't have posted any more until I had
dug more into "maximum entropy production." Perhaps I put a little
too much trust in the "experts." I will dig a little more - later.
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