Meanings in this exchange do not seem well anchored, and so I am compelled to retreat to some basic semantics just to keep my balance.

For one thing, the word "determinant" strikes me as having a range of meanings. For example, it seems it can refer to either a state of being or to a kind of relation, to ontology or epistemology.

As for state of being, it commonly seems to refer to what is the opposite of Absolute or ideal, to what is spatio-temporally contingent or subject to change. It is my sense that the consensus in science today is in favor of an ontological monism, also known as materialism, in that everything is contingent. In this sense, nothing is ontologically indeterminant. For example, in a EM field a measurable value at any spatio-temporal point is an unactualized unequivocal possibility. So this modal possible value is real and determinant. 
 
As a relation, the word determinant often refers to a causal relation, although we then we have to consider whether this might be unequivocal determination or probabilistic determination. More importantly no one really knows what causality is, and so it usually refers to a predictable relation between proximate events, a generalization of experience that lends confidence to predictions. That is, it is epistemological rather than ontological and so irrelevant to your final question.
 
I also have trouble understanding "ignorance of fundamental entities",

a) Ignorance seems a fact of epistemology rather than ontology. That is, can we infer any ontological truth from ignorance except the reality of our own ignorance? (this seems to stand  poor Descartes on his head ;-).

b) I'd be inclined to argue that all things are processes and that hypostatized "entities" are only a hypothetical limiting case. That is, while the hypothetical "entity" may be conceptually useful, it does not actually exist.

c) Further, I have no idea what would make an entity "fundamental". Does this word imply an ontology of systems and hierarchy of levels? If so, I'd be skeptical, for system and level seem only to be methodological tools that at least offer a one-sided distorted  view of things. For example, why is one level privileged as "fundamental" unless it is epistemologically convenient (supports the reductionist explanation suited to hypothetically "closed systems")?

I admit this just raises more questions rather than address your own. So let me try to do that, even though you probably won't care for its presuppositions. An example I'll use for ontological indeterminance is any "process".

I would follow Aristotle somewhat and define process as the union of the modality of possibility and the modality of actuality (this modal realism seems to be the consensus these days in the philosophy of science). Not really unconventionally in substance, I would define this union as the constraint of the probability gradient (usually spoken of as the energy gradient), arising from the improbability of any actual structure, on its possible alternative states  to constitute a probability distribution. If this process enters into union with another (such as measurement instrumentation) there emerges from that union of probability distributions a novel actuality known as a property value. While this does get a little hairy, at least it starts from a scientific consensus over what seem ontologically indeterminant.

If for some reason you followed this paragraph carefully, it returns an ambivalent answer to your question. That is, ignorance (or any other relation of a process) means that its probability distribution in hypothetical isolation lacks actual values and so might be called indeterminant in some sense; actual values are the creation of measurement. On the other hand, isn't a state of pure possibility unconstrained by actuality called a perfect vacuum? If so, a perfect vacuum would be ontologically indeterminant, although it couldn't properly be called a system.

Haines