Many systems behave with very exact determinism. The circling planets and a sphere rolling down an incline were examples that attracted applied mathematical treatment in the early days of modern science. When it became apparent that humans were systems built from the same stuff as inanimate objects it came to be thought that the behaviour of humans must be exactly determined. If you could know the exact state of the person then that persons responses could be exactly calculated. This was interpreted to mean that people don't have free will.
Then came the quantum revolution. Systems don't have exact state. The state of a system and its evolution are only determined statistically, not exactly. This was seized on by some as restoring free will.. This never made any sense to me.
Instead of mapping out a persons exact future, we can instead only map out the probability of all possible futures. Or if you prefer the multi-worlds interpretation then we can map out all the person's futures and how frequently each occurs. It is a mystery to me why anyone feels that this bestows any more free will than the more exact Newtonian determinism.
The problem of free will comes from the intersection of the ideas of science with the idea of an infinite God. God is envisaged as being able to do infinite amounts of calculation at infinite speeds. If we remove the idea of an infinite God then the problem of free will disappears.
Lets suppose that we wish to solve the problem at the heart of the free will issue. We wish to enter the state of a person into some computing device and extract information about the future behaviour of that person. If a person was as simple as a perfect sphere rolling down an incline then we would expect an easy and definitive result.
One possible way to address the problem is to make an exact copy of the person and follow the behaviour of that copy. Effectively we are using a human as a calculating device giving back information about human behaviour. A key question is: can we do better? Can we build a simpler system which will predict the behaviour of the person. Science now understands the butterfly effect: where in unstable systems small changes to small parts rapidly expand their effect to alter the macro state of the total system. Mathematically we now also understand that most information, such as the information describing the state of a person, is incompressible -- it can't be described by a simpler system.
It thus seems overwhelmingly likely that you can't build a simpler system to determine the evolving state of a person. What this means is that the only effective way to find out what a person will do in a given situation is to put that person in the situation and see what they do. To rephrase that:
Observing what a person does is the only way to find out what that person will do.
To me this expresses the fact that the person has free will. The person's actions are not "determined" in any physically meaningful sense.
There is a problem with this interpretation. It also applies to hurricanes and bacterium. Clearly a hurricane doesn't have free will because it doesn't have will at all. A becterium, like a person, does act purposefully to decrease local entropy. If you don't want to allow that a bacterium has free will then the next step up is to creatures which have specialized cells used for decision processes. It seems unlikely that this is a hard break. Probably as soon as there is some cell differentiation then some cells are more concerned with decision and others less. And from there to people there is no clear cut point where we could reasonably divide those with free will from those without.
Sadly even the break between life and non-life is not that clear cut. Perhaps we are forced to the straight forward view that some things have more will than others. Will is always free will because the extent to which a systems actions are predictable by a simpler system is also the extent to which we would not identify something as really displaying will at all. We thus return happily to the sensible view that prevailed before the imaginary monster of determinism arrived on the scene.
 somebody, probably Chaitin, proved "nearly all information is incompressible" or something like that.