Identify what fallacy this is, "Our bodies are nothing but atoms and molecules, and such things are bound by the laws of physics. Therefore, all of the actions of our bodies must be determined by the laws of physics."

Reasoning issues involving whole to parts, or parts to whole, are fallacies of composition/division. However, it is extremely important to keep in mind that these particular fallacies do not state that what is true of the parts can NEVER also be true of the whole—rather that it is not NECESSARILY true of the whole.  It may very well be at times that what is true of the parts may indeed be true of the whole.

Your example here fits this idea according to classical physics:

As we belong to the set of “local presentation of the universe” we are bound by its parameters. Such parameters can be described as laws of “physics.” One such parameter is causal determinism (i.e., a present state determines a future state.) Everything within our set is bound by this determinism. To try to use a claim of composition fallacy to show that this is necessarily NOT true…is a fallacy.  

This is the fallacy of composition , the idea that what's true of the parts of something must be true of the whole.

I see a non sequitur, questionable premises, missing quantifiers, and some undefined terms that can lead to confusion, lack of clarity, or even invalid conclusions – i.e., bad arguments.  Re-arranged as premises and conclusion, the argument could look like:

Premise 1: Our bodies are nothing but (i.e., contain only) atoms and molecules.

Premise 2: All things containing atoms and molecules are bound by the laws of physics.

Conclusion: Therefore the actions of our bodies are determined by the laws of physics.

Premise 1 is questionable in that atoms and molecules themselves have constituent parts meaning that our bodies also have those sub-parts of atoms and molecules so the "are nothing but" part becomes false.

Premise 2 would be clearer if we knew whether it means "bound by laws of physics only" or by "laws of physics in association with other laws".  

Premise 2 and the conclusion would be clearer with a quantifier.  Which laws of physics are referenced in this premise?  Are our bodies' actions determined by all laws of physics, by some (but not all) laws of physics, or by just one or two?  

Premises 1 and 2 speak about the composition of our bodies and premise 2 adds the notion of being bound by certain laws.  The conclusion jumps to "actions of our bodies".  This non sequitur opens the door to an invalid conclusion.  [It's possible, for example, that parts of our bodies might generate heat (a law of physics) without moving (producing an action).]

While the set of statements above form a questionable argument, a more valid (but probably less useful) version might be:

P1 – our bodies contain lots of atoms and molecules

P2 - all atoms and molecules react in accordance with many of the laws of physics

C  – our bodies react to some of the laws of physics.