I find this "protectionism" of the term evolution more and more interesting. I suspect that underneath it is a concern for a loss of control over a claim to empiricism.
Which protection? That I don't want to be confused by biologists or to confuse them by speaking about the evolution of the state of physical systems (after all, there is already enough confusion between terms common to both evolutionary biology and areas of machine learning which borrow extensively from living systems but then sometimes use the terminology differently)? Or that I don't think confusing the public further is going to help anyone?
Lots of terms are used in specific ways in specific fields. Public misconceptions of science (and even some misunderstanding among certain fields) is common place enough because people often conflate general meanings of words with technical ones. You see this in creationist writings, popular science, pseudoscience, and beyond.
Evolutionary theory is quite vast and quite old (most fields around today in biology and the life sciences weren't around when Darwin lived). While much is firmly established, there continues to be areas of active research across different fields from neuroscience to theoretical chemistry and astrobiology. Evolutionary theory provides the framework and foundation for much of the research here, including research that seeks to alter or extend or knowledge of evolutionary processes.
The last thing we need is to promote a view which not only encourages widespread misperceptions of the nature of evolutionary theory but actively seeks out ways in which to mislead or confuse others by conflating the terminology used in evolutionary biology and related fields and both "evolution" used more widely and as it is used by the layperson.
Evolution in general tends to imply some manner of direction or goal-oriented nature, and indeed in evolutionary algorithms the entire point of borrowing from evolutionary biology is to use models of evolutionary processes to obtain particular goals, which is antithetical to the kinds of uses of randomness (both in terms of natural selection and beyond) we find in biology. The "evolution" of the cosmos or universe or Earth is at the very minimal a global tendency, while evolutionary processes in biology are fundamentally localized. Researchers already have to go above and beyond whenever they wish to support a view in which certain features, tendencies, patterns, etc., tend to characterize evolutionary processes
in general because they already need to make clear distinctions between theories concerning the origins or nature of these patterns found in evolutionary processes and evolutionary theory itself.
What you seem to seek is well beyond this or even beyond those who would suggest that evolution itself can in certain ways be seen as directed towards e.g., greater complexity or thought of in more global terms than the actual processes that take place. It is to take a simple idea as to what evolution tends to mean in common parlance, equate this with the sense used in biology, and then make connections with quite general descriptions or ideas from a wide variety of fields regarding (it would seem) anything that tends to change over time.
But these phenomena are often radically and fundamentally different.
And there is a real concern here I think because we have science that describes the limitations of mathematics when trying to understand physical systems which are subject to non-linear iterative processes such as the ecological evolution of species.
Yes, difference equations can be insoluble, and in general so are differential equations. And both nonlinearities and high dimensional spaces make even the appropriate approximating numerical methods highly non-trivial or even impossible. But these situations (i..e., those in which the governing equations or distributions or systems are nonlinear and the number of variables, particles, functions, etc., is large) are common to QFT, signal processing, economics, statistical physics, cognitive neuroscience, aerodynamics, and on and on. In QFT and statistical physics,we're always solving integrals in dimensions so high even understanding what kind of generalized volumes we're working with becomes all but impossible. The divergences encountered in particle physics and QFT can't be regularized in any consistent manner in general (and when they can it can take a lifetime to figure out how to carry out a small number of calculations). Elsewhere we are plagued by the "curse of dimensionality" (perhaps most especially in the social and behavioral sciences) simply due to the high number of variables. Across fields and in applied math, it is basically always the case that we run into situations in which difference equations can't be well approximated by smooth functions or manifolds that can be integrated over. In these cases and more generally, a great deal of work is typically needed to figure out just how to approach finding a way towards a solution.
Thanfully, mathematicians and scientists have been working on these problems for a very long time. There are entire fields devoted to the kinds of problems one faces when dealing with complicated (nonlinear) signals (discrete or continuous). Most of the work in applied statistics (and all of "big data") concerns finding ways to work with systems in extremely high dimensions without massively ignoring issues such as multicollinearity and dependence or the loss conceptual clarity gained by dimensionality reduction methods such as PCA. Feynman diagrams and an a slew of linguistic devices have been employed for decades now in areas like HEP, statistical physics, condensed matter physics, and similar fields where it will never be possible to even approximate solutions to the evolution of systems even when we know the required integrals exist (they typically don't) because there are just too many equations governing too many "bodies" in the collective for computers to work out answers before the end of the universe.
Sometimes, work in some of these problems leads directly to progress or at least use in other fields. We see this especially with statistical methods. Perhaps more frequently, attempts are made to employ methods (especially if they sound sexy, such as anything with the word "quantum") in fields they were never attempted with little or no progress, such as in most of "econophysics" or in quantum models of cognition.
I don't see how confusing the use of the term "evolution" more than it already is currently being confused all too often is going to help anybody very much. It's not as if evolution comes equipped with a single mathematical tool, framework, approach, or scheme. Research in this field and related fields has made use of or developed a variety of mathematical tools, many of them found in systems sciences or fields that deal in particular with complexity. On the other hand, in work on complex systems we find researchers working with fuzzy sets, expert systems, non-classical probability, and a swathe of other approaches that aren't of much use in evolutionary biology.
So you have on the one hand the fact that much of the mathematical tools that you seem to refer to is being and has been developed elsewhere both thanks to evolutionary biology and independently of it, and on the other the fact that these tools are not sufficiently general for all the work being done already in systems science and complexity research. So, again, I don't see what is to be gained by claiming that the term "evolution" in evolutionary biology "not just about life." It is.
I think that biological evolution is to systems and complexity science is as physics is to Newtonian determinism.
How? Newtonian mechanics isn't deterministic except insofar as differential equations are. It is when one attempts to generalize the deterministic character of Newtonian mechanics
beyond where the formalism allows, i.e., to systems that aren't isolated. And furthermore much of complex systems comes from the application of these very laws as they are the differential equations whose nonlinearities lead to much of the kind of complexities you seem to wish to refer to.
Physics once paired with empirical observations and mathematics became the archetype of science in general. The hard sciences were thus born and scientists could set up equipment in a lab and get good work done.
I don't buy into the hard/soft distinction. In most physics, the empirical work is done by the "experimentalists" while the mathematics and theories are worked out by theorists. Historicall, mathematics wasn't seperated from either natural philosophy or the physics it became.
Of course as discoveries in physics were made the gradually led scientists outward toward other topics that were not so amenible to a lab.
They started out there. In data science and in meaurement sciences much of the original work came from the earliest social scientists. In physics, similar work and more was done in the lab only in the sense that telescopes were considered to be in labs. It was all observational, not controlled labratory work. That was mainly what came to be chemistry and was some ~200 years later.
Earlier still, theologians and philosophers worked on developing the probability calculus and formal logics for use in betting.
All this is to show up the triumph that is science as modelled by the empirical lab experiment as well as the challenge for science where the lab is hard to attain.
Most of they physicists I know greatly respect experimentalists but do not consider their work to be as important because all they do is too empirically check what the theorists postulate, and usually they can't work out how to do so for a long time (decades, typically). Similar trends are now found in theoretical biology and chemistry where more and more work is done in fields that don't involve labs so much as whiteboards and coffee with some help from python, mathematica, or something similar.
Evolutionary biology is to systems theory as Physics is to science
It isn't. I know of at least two well established approaches to biology that are different in their outlook but both are explicitly under the umbrella of
systems biology. Systems sciences abound in physics, chemistry, biology, neuroscience, sociology, engineering, etc.
This isn't labs vs. the next generation of science. I don't know anybody working in physics or in systems sciences or elsewhere that unnecessarily and artificially divides scientific research as you seem to be doing. Nor do I understand why you are doing so.
But evolutionary theory rests on an abstraction which is now becoming more and more evident: systems theory.
It doesn't. Partly this is because much of what is shared is due to direct borrowing in systems sciences from earlier work in evolutionary biology, which means that systems theory rests on this work not the reverse. Partly this is because systems sciences involve a vast array of paradigms which aren't found in evolutionary biology, from much of the work done in network science (which is used a lot in some areas of biology but not so much in evolutionary biology so as to much distinguish it from basic graph theory) information theoretic approaches to complexity. Partly this is because there is no singular systems theory but a wide array of concepts that have now been well developed (or abandoned, in certain cases such as catastrophe theory or similar fads) and are used across the sciences which are all interdisciplinary and have been tending away from isolated research groups in particular departments to interdepartmental institutes and the like. Partly because you have your timeline backwards.