[EDIT: My question can be refined to, how does Heron's account of the behavior of light fit into a classical causal account of nature? Especially, is his account a kind of natural locomotion in which light "striving" for the shortest path qualifies as a kind of final cause? Or if not, what kind of explanation is it? Or does it find no home at all in an Aristotelian physical framework (which would be hard for me to believe)? I fear that mentioning modern physics in my question below was a distraction -- it was the context in which the question arose for me, but is not really essential.]
Much of modern physics can be written in terms of so-called variational principles. One common example is Fermat's principle of least time: out of all the ways that light could get from A to B, it chooses the quickest route. And so on, to Lagrangian and Hamiltonian formulations of mechanics etc.
I came across a physics text that claimed, casually and briefly, that such principles are final causes in the Aristotelian sense.
I am looking for a second+ opinion/elaboration on that claim. To what extent would the classical tradition (Aristotle, Aquinas) really accept such a variational principle as satisfying the definition of a final cause?
I have found numerous quotes in secondary literature of ancient or medieval authors who ascribe an economical character to nature's workings. A significant example is Heron of Alexandria who not only claimed (in a predecessor to Fermat's principle) that light "strives to move over the shortest possible distance, since it has not time for slower motion" but drew quantitative conclusions from this principle. Another is Grosseteste, also in the context of optics, "nature always acts in the mathematically shortest and best possible way."
Did these authors understand principles like this to be expressions of final causality, or something else? Ideally, is there a passage where a classical author explicitly considers whether such a principle -- likely Heron's -- is a final cause, or clearly treats it as a final cause or as not a final cause but something else?