Re: Complexity Explorer

Posted by Roger Critchlow-2 on
URL: http://friam.383.s1.nabble.com/Complexity-Explorer-tp7586215p7586222.html

We have had discussions on this many times, and the usual result is that everyone gets fed up with all the technical details that need to be kept sorted out.  There are equilibrium vs non-equilibrium systems, classical vs statistical thermodynamics, closed vs open systems, statistical mechanics vs information theory, and so on

The MaxEnt that Simon is teaching is the only one usually abbreviated as MaxEnt by its practitioners in an attempt to keep it from getting confused with the other discussions.  It's the practical procedure that grew out of E T Jaynes observations about probability theory and physics.  It essentially says that if you repeatedly make observations of a system and you correctly model the constraints on the system, then your observations should follow a distribution with maximum entropy of the statistical/information theory variety.  The usual example is observing dice throws which should equipartition themselves over the six possible outcomes.  If your observations converge to something other than this MaxEnt equipartition, then you should conclude that the dice are loaded and strive to improve your model.

That non-equilibrium systems maximize entropy production is a conjecture which can be defined and actually works for a very small proportion of non-equilibrium systems.  Basically, take the non-equilibrium systems that are so close to equilibrium that they barely do anything at all, and you can see this principle in action.  Push the system a little further from equilibrium and all hell breaks loose.  What that means for everything else in the world awaits an expansion of the theory which has been pending for almost a century now.

-- rec -- 

On Sat, Jun 13, 2015 at 12:28 AM, Russell Standish <[hidden email]> wrote:

On Sat, Jun 13, 2015 at 06:12:16AM +0000, Russ Abbott wrote:
> Although I haven't gone through the MaxEnt tutorial I have a question if
> anyone would be willing to think about it.
>
> As I understand it, one aspect of MaxEnt says that nature chooses that path
> that maximizes entropy production -- and that satisfies whatever
> constraints exist. (Or something like that. I don't claim to know enough
> about it to say anything definitive.) Yet when I think about the earth and
> the way it deals with the energy it gets from the sun, it seems to me that
> the biosphere "does its best" to minimize the rate of entropy production.
>
> If there were no life on earth, all the sun's energy would be quickly
> radiated back into space, mostly as heat and some as reflected light. That
> seems like the fastest way to dissipate the sun's energy and produce
> entropy.
>
> With life on earth the sun's energy is absorbed and "exploited" to the
> maximum extent possible. That's what life does; it looks for and fills
> unexploited energy niches. Eventually the remaining energy is radiated back
> as heat. So that would seem to slow entropy production.
>
> Even more telling, much of the sun's energy is stored on earth as
> energy-rich organic material left over biological organisms die. So some of
> the sun's energy is never sent back to space -- until that stuff is burned.
> So that would reduce the rate of entropy production even further.
>
> Is this a reasonable way of looking at what happens? Is this inconsistent
> with the notion of MaxEnt? Or am I misunderstanding something?
>
> -- Russ

It's been a decade or so since I read the MaxEnt literature, but from
what I recall it is largely a physical principle, eg it describes
things like the formation of Hadley cells to assist in the transport
of energy between the equator and the poles.

But it does seem plausible it ought to describe living systems too. In
the fossil fuel example you allude to earlier, life is currently doing
its darnedest to maximise the entropy after unlocking the excess
negentropy locked up by geophysical processes. (ie burn, baby burn!).

But I don't know of anyone who has succeeded in applying MaxEnt to
information systems (such as biology) - I thought I'd try myself, but
like with so many good intentions, life has intervened :).

Cheers
The other Rus.

--

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Principal, High Performance Coders
Visiting Professor of Mathematics      [hidden email]
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