Re: Nature of Counting and FIS

At 02:30 AM 07/10/2002, I wrote:

>A second way that extremal principles have been suggested for living
>systems is the principle of entropy production maximization (MaxEntPro).
>This is a global principle proposed first, I think, by Rod Swenson, though
>one can read a version of it back into Jaynes. It seems to violate PLA
>very seriously. Anyway, Schneider and Kay have proposed an extension to
>thermodynamics according to which systems use every means at their
>disposal, including reorganization, to approach as closely as possible to
>equilibrium. They claim to have evidence for this from ecology, though I
>find the evidence ambiguous.

I should have pointed out that S&K do not relate their principle to
MaxEntPro (so far as I know), and that Eric Schneider expressed
considerable skepticism about MaxEntPro when I last talked to him about a
year ago. He showed me the work on the Earth's atmosphere. However, some
have interpreted their claim that living systems to degrade energy
gradients as implying MaxEntPro, at least for such systems. Anyway, I do
not want anyone to think I am foisting MaxEntPro on Schneider and Kay, or
that I think that they accept it, or that I think that they should accept
it. Sorry for the comment on my own post, but this is a tendentious issue,
there will be talk about it in the near future in popular terms, and I
needed to make this point. The following are some formal caveats. I think
there is something exactly right about the K&S principle, that it is a form
of extremal principle, but that it needs to be expressed more clearly and
carefully. In particular, I think that the very means by which gradients
are degraded feed back into those means themselves, so the principle can be
applied only locally and for short times unless certain global conditions
hold, and that their (K&S) principle does not imply global rates or states
in itself. In particular, it does not imply MaxEntPro except possibly when
the means of producing means are not reflexive or are entirely internal.
Jerry's objections mention the latter, but I think the former is required
as well -- I would guess that he assumed it because it seems pretty
obvious. However, if optimality applies only to functions, the
interactivity assumption (relevance of flows between external and internal
processes to optimality issues) is violated by autopoietic and
operationally closed systems, and at least some people don't find
interactive flows to be relevant to optimization problems -- the
organizational problem, for them, is to optimize for all flows in and out,
so the values of or changes in the values of the flows themselves serve no
function -- regulation is all focused internally. I think that organisms
violate exactly last this double (logical sum) condition, that is, the
means are reflexive and they are not entirely internal. I say "possibly"
because I think even then the principle does not necessarily hold, but I
have seen arguments that try to set the constraints so that "by all means
possible" is restricted to those that do not constrain entropy production.
I think that this trivializes the optimality involved, but I am not going
to argue that here.

Again, sorry for the complex and rather formal caveats.

John

>The important point for this group is that, like MinEntPro, it allows
>information to be reduced out. Schneider is quite clear about this
>implication in his recent writing. MaxEntPro systems are obviously highly
>non-Hamiltonian (highly non-conservative), but there is a sense in which
>they are very mechanical like, because of their extremal behavior. One
>system that approaches MaxEntPro is the Earth's atmosphere, and fluid
>vortices in general. it is precisely their lack of stable structure that
>allows this. (Recent empirical work suggests that the Kolmogorov
>hypothesis of self-similarity of vortices at all scales except the larges
>is actually false at small scales, so perhaps event the atmosphere case
>does not really fit the MaxEntPro model.)
Received on Mon Oct 7 09:13:46 2002