I would look to Global Workspace Theory, on why we have a unified singular awareness, it is the workspace, or 'desktop' of mental processes, with different subroutines competing for attention & integrated there - if you look at convolutional neural networks, essential to developing digital vision processing we can picture how this happens. Split-brain patients also, show the multi-agent nature of our brains, with one hemisphere tilted towards modelling ourselves, one tilted towards modelling the environment.
I would like to take a moment to point out, that in a reductionist physicalist-materialist determinist view, the distinction between ourselves & our environment is strictly speaking, an 'illusion'. But this gets at why stating this doesn't add content. We are atoms, the world is atoms, there is no fundamental substance differentiation. But, it is a useful conceptual distinction to differentiate the lump of phenomena we call body & mind, which have persistent traits while alive, from world, which is far more variable.
So the workspace integrates data, piecing the information from our tiny points our eyes focus, with fuzzier images in peripheral vision, & processing like edges & depth perception, into a mental model that gives persistence to things not currently seen or focused on, and integrated with our dispositions & concerns - Donald Hoffman is great on Do we see reality as it is? & how evolution will supply motivated information aimed toward successful reproduction, over dispassionate 'objective' data. We need tools like examining cognitive biases & consilience to make our models better. So this is the explanation of simple awareness anyway.
'Free will' is a conceptual framework or picture, that involves self awareness. I would look to Hoffstadter's strange loops to understand the significance of this. By having a self-model in the model of reality, we can amend or develop who we are, in relation to expectations about the future, informed by conceptual information gleaned from the past - that is, pictures of the past which sieve out noise (see salience landscapes). With a self-concept in the 'loop' a new behaviour occurs, feedback. A self can be situated towards the future, making decisions founded on an illusion, that of speculative histories: if I had done otherwise different thing/s would have happened. But you could not have done otherwise, that is the determinism. By holding models of the future in our brain, future timelines become more complex: harvesting of Gibbs free energy can be maximised, ie the hallmark of life, can be maximised. We expect to be able to identify distant aliens using this principle, both insentient & sentient, by degree of efficiency.
Evidence for the mechanism of developing a self-concept, can be found in mirror neurons. These help organisms model their bodily motions on those of others, to help with learning. They are far more present in social animals. And I would link them to intersubjectivity and the metaphor Indra's Net. The feedback between self-concept, and 'reading' others as though they had it, deepening the complexity of the mental model. The complex intelligence of largely solitary ravens & octopuses, illustrates problem solving intelligence seems to be on a different track. But conceptualising intelligence & language, how noises from our faces evoke things in the minds of others, hinges on intersubjectivity. Dunbar's number shows our neocortex relates to social group size, and allows impulse inhibition in relation to our social world.
So this is how I picture free will, in a compatibilist way. Free will is a 'useful illusion', like having a self separate from the world. It depends on a mental model based on the 'lie', that we could have done otherwise, which none-the-less produces real insights, which we cannot model human behaviour without.
The last piece of the puzzle, is incomplete information. Sensitivity to initial conditions, means even small discrepancies can have unpredictable scales of consequences. Conceptualising others as having personalities, rather than trying to predict their atoms, illustrates how much more efficient an explanatory layer can be, one we picture as supervenient. Whereas uncertainty about position & momentum of atoms rapidly invalidates a model in that 'fundamental' layer, the explanatory layer is far more robust, and efficient (ie, 'personalities').
Epiphenomanilism like the Chinese Room argument, is invalidated by the physical reality of information, as shown by the explanation of why Maxwell's Demon can't violate thermodynamics. Thoughts cannot be free-floating 'spandrels' that don't relate to fundamental realities, they are deeply related to and reflect them, in ways that sift out noise toward selecting outcomes from models of probability space.
QED.
