I liked it. But I'm not sure I would call the Earth an organism. Anyway, the argument is pretty good and it led me to these ....
THE PHYSICS AND MATHEMATICS OF THE SECOND LAW OF THERMODYNAMICS
Caratheodory's Principle and the Existence of Global Integrating Factors Abstract. A proof is given of a theorem on the integrability of Pfaffian forms which is used in Caratheodory's approach to thermodynamics. It is pointed out that Caratheodory's original proof of the existence of entropy and of absolute temperature is incomplete, since it fails to take into account the local nature of this theorem. By combining the theorem with the results of BTJCHDAHL and GBEVE on the existence of continuous empirical entropy functions, it is shown that the First and Second Laws of Thermodynamics imply the existence of a globally defined differentiable empirical entropy function for every simple thermodynamic system. This result supplies the missing step in Caratheodory's argument and makes a separate proof of the principle of increase of entropy unnecessary.
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An advantage of this approach is that no separate proof of the principle of increase of entropy is required [3], since the true entropy is a strictly increasing function of the empirical entropy obtained here.
In section 2 we demonstrate the existence of a continuous (global) empirical entropy σ by methods similar to those of BUCHDAHL and GKEVE [6], but without assuming the Second Law of Thermodynamics. The First and Second Laws are introduced in section 3 together with certain supplementary smoothness assumptions, and it is shown that a differentiable local empirical entropy can be defined in the neighbourhood of each point of M. The construction of a differentiable global empirical entropy s is finally accomplished in section 4.
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Since g is a strictly increasing function it follows that the C°° map s = go a of M onto {(0, oo), <$} is a C°° global empirical entropy on M. Moreover s has no critical points, i. e. ds never vanishes. For s may be expressed on each set V of the open covering i^ of M as a strictly increasing C°° function of the corresponding C°° local empirical entropy sv, and dsyis everywhere non-zero on V. It follows from (E) that ψ = λds, where λ is an everywhere non-vanishing C°° function on M whose reciprocal is thus a global integrating factor for ψ.
Some of the characters in the paper are not rendered correctly above so you must read the paper to see what they are, and I hope I did't screw up anybody's arrow 3 because of the bad rendering.
As an "aside", Rosen hits a few "sore" points, namely, "meaning" and "information" which involve arrows 3, 2, and 4.
Instead of “Rosen”, I should have written “Mikulecky”.
Yeah. Shades of "Gaia theory" there. And yet some scientists not committed to this theory are finding that the biosphere as a total system does seem to possess "lifelike" features or qualities....
You wrote: "Rosen hits a few 'sore' points, namely, 'meaning' and 'information' which involve arrows 3, 2, and 4." I can see that such things may be "sore points" for people whose thinking is structured by the Newtonian Paradigm. :^)
There's another article that deals with these matters, but evidently it doesn't exist anywhere on the Web these days. That is John J. Kineman & Jesse R. Kineman's "Life and Space-Time Cosmology." It is very much a development of Rosen's core ideas.
I found it fascinating. Its geometric foundation in the formalism of a "Euclideanized" complex Minkowsky space and imaginary numbers (where the imaginary parts refer to time as mapped on the imaginary axis) seems a very secure and solid basis for the model, and thus for inferences amd demonstrations that can be drawn from it. I particularly liked the idea that there is an observable "real" universe and an abstract "real" universe, from the latter of which formal causes arise in the natural world. I'm delighted that people are beginning to speak of formal causes again — and also final causes, though the Kinemans do not seem to make the latter explicit in this work. In my humble opinion, for too long has science restricted itself to material and efficient causes only! Plus I really liked the idea of a fifth "time-like" scalar dimension as the context in which the observable and abstract worlds subsist and "resonate" with one another. It was also very interesting to see the way the Kinemans seem to extend the Bohr complementary principle to incorporate the idea of a mutually causal entailment.
If you'd like to see it, just FReepmail me.
Thank you ever so much for writing, AndrewC! And thanks for the link to "The Physics and Mathematics of the Second Law...." I'll go study up!