"How does the Aristotelian/Thomistic conception of the soul and the body and their relation to each other resolve the problem of free will and determinism? How does the Thomistic soul/'form' redirect certain neuroparticles and thus intervene in the otherwise completely deterministic neurological pathways in order to produce the desired response? If they don't, there's no free will. Additionally, if they do, then they violate the fundamental physical law of conservation of energy."
A few other readers engaged the question, but mostly on the front of challenging the notion of physical closure and determinism. I took a different tack by trying to address the apparent conflict head-on.
I take much of the 'point' of A-T anthropology vis-a-vis physical causation to be that, while there is no question of a non-physical cause for bodily motion, in secondary terms, there is the larger principle that no body is 'just' a material body. As in: action is a response to perception but perception is mediated by sensation, conation, imagination, and, in the case of rational animals, intellection. These perceptual filters generate varying degrees of deliberation in their bearers, i.e. a proper range of action potential for various organisms. Amoebae have a very narrow range of sensible deliberation which can modulate there perceptual being-in-the-world, and higher animals have a correspondingly broader range of action. n Rational animals such as ourselves, by virtue of the intellectual judgment of universals in particulars and the good per se in being per se, have a deliberative access to a range of potential which transcends the deterministic bounds of purely physical causation. When a perceptual experience is given a value in the larger intellectual noesis of a human, the response is something which transforms an otherwise strictly indeterminate action potential into a concrete action, which eo ipso modulates how the physical organism responds to the physical stimuli. We don't experience the world "raw", and therefore we can modulate the incoming data; conversely, we don't respond separately from the entire Gestalt of our own (social-physical) place in the world, an entirety which just as seamlessly modulates our inner physical 'world'.
The bottom line seems to be this: Physical motion is not rational. Human perception and action are, however, rational. Humans are also continuous with the world of physical motion, but the power of our rational nature makes it the case that otherwise irrational physical matter responds and acts rationally, which is pretty remarkable.
Imagine a child who grows up seeing and handling triangles in his house but is never instructed as to what "triangle" means. One day, though, he is told the meaning of these objects and his entire world changes. Nothing physical about him or the triangles changes--there is no Cartesian 'gap'--, but everything about his perception and action has been transformed. Otherwise meaningless matter has been "de-potentiated" and "in-formed" such that his entirely 'materialistic' existence goes on as before, yet his actual, proper existence is qualitatively different. Perhaps you all know Polanyi's metaphor of the scribbled line suddenly becoming intelligible words and then flowing back into random scribbles. From nonsense to sense back to nonsense without a single physical break.
The larger doctrine of habits/virtues point to this fact by saying that recurring de-potentiation of one's body and environment leads to qualitative changes in both of them, yet without corrupting their physical contiguity/history in an otherwise a-virtuous world.
I have already tried to explain how intelligible order 'subvenes' (as it were) physical closure without violating physical order. I would simply like rephrase the question in order to show how Aristhomistic makes sense in a, perhaps disappointingly, plain way.
"How does the 'form' of a number redirect certain microparticles and thus intervene in the otherwise completely deterministic physical pathways in order to produce the intelligible content?"
Two, as a pure intelligible, makes otherwise meaningless, but physically 'taut', matter into an intelligible reality. No violation of physics, nor a physicalist reduction either. I can't "explain how" intelligible form "does" what it does, but I can't deny that it does what it does, and that this achievement is an analogous primer for grasping how soul orders body.
Actually, one commenter's reply to the question was in the same spirit as mine, and led to an increasingly lengthy tangential discussion of numbers, definitions, form, descriptions, etc., about which I shall write in the near future.