Atheist here: I’m of the opinion that most of the confusion in the free will debate comes from badly-defined terms, which spring directly from the fact that the free will debate started as a religious discussion.
In religion, “free will” means “God isn’t determining your choices and actions”. The presumption is that in the absence of free will God, or the gods, or the fates, have tied magical puppet strings to you and are consciously manipulating events toward an end that they have determined should happen. Free will, on the other hand, means that you make your own decisions, which results in you at least partially causing your own outcomes.
Then you add atheists into the equation and they take God out of the equation, that puts a giant hole through the definitions. By a straight read of them the answer is “obviously we have free will; God/gods/fate isn’t determining our actions because there aren’t any God/gods/fate to determine our actions. We must be making our own choices because there’s nobody else to do it for us”.
Of course, this makes atheism sound better than theism, so we can’t have that. Therefore we have to change the definition where atheists are concerned so that atheism sucks again. Well, that or the theists were so incredibly stupid back then that they really came up with the following stuff by accident:
To make atheism suck, or just because atheism really confused them, the decision was made to define “physics” as “god”, swapping that into the definition.
Given a definition of “physics isn’t determining your choices or actions”, atheists have no choice but to honestly answer “Of course physics determines our actions; everything is physical and determined by physics.” (Theists, of course, pretend that their brains are powered by magic which gets around this.)
The thing is, though, that definition is stupid. The real issue with free will is whether you’re somebody else’s puppet. But in the atheism model, the “physics” which determine your actions are your own body. By any non-idiotic interpretation of the situation, your body, your brain, is you. That’s what any sensible compatibilist approach boils down to: noticing the obvious fact that, physical or not, our bodies don’t have puppet strings sticking out of them. We say that free will is compatible with determinism because deterministic physics were never the problem to start with. The problem was God - external forces outside of us reaching inside and controlling us.
Atheists don’t have that problem. Our brains are physical organic computers, which are demonstrably mostly or entirely deterministic in function. They control us, providing a will that is free of outside control. And that’s that.