I am not sure about how to approach this thread topic, but only because I don't know what Rousseau thinks of as a "scientific definition". I certainly understand what a technical definition is, because I have worked on those for years.
Maybe 'scientific explanation' is a better way of wording it than 'definition'. Via scientific methodology we can uncover many tangible properties about a human being. We can deduce that cells have membranes and metabolize ATP. We now understand what the nervous system is and, roughly, how it works etc etc.
But free will or it's lack isn't actually a tangible property of a human being, it has no, and can't have, a scientific explanation behind it, because it's a semantic construct that's been stretched much too far, beyond the bounds of it's literal meaning.
I doubt the value of that kind of reductionist approach to explaining the nature of free will. The following lays out the essentials of my compatibilist approach to free will.
The concept of
free will depends on the fact that human beings are ignorant of the future, which is indeterminate at the point they are making a choice. The future (
irrealis) is only a set of imaginary outcomes of an action. Therein lies the choice. Hard determinists argue that there is no choice, because, once the future is known, the agent could not have acted otherwise in actuality. The problem with that is that hindsight is always looking into the past, which is known (
realis). We can easily imagine having made a different choice, if circumstances had been different. If only we had known then what we know now. Hard determinists have created the illusion that there is no actual free will, because they confuse realis--fixed knowledge of reality--with irrealis--imagined realities. They ignore the imagined realities, because those never happened except in the agent's imagination.
As a linguist, I know that every language on record makes this distinction between realis and irrealis in its tense and mood systems--usually manifested in markings on verbs--in English, past and present suffixes for realis and modal auxiliary verbs for irrealis. Other languages can mark this distinction in different ways, but it is always there. This distinction is therefore a feature of basic human cognition.
Free will is an essential aspect of human behavior, because it is the yardstick that we use to assign responsibility to human beings for their actions. People are, and should be, held accountable for their actions. That is how they learn to fit in with human society. The problem with hard determinism is that they often attack the concept of human responsibility in their efforts to dismiss the concept of free will as merely an illusion. Free will is real, because selecting among imagined future outcomes is a real choice in the mind of an agent at the point in time when the choice is made. What makes a willful action "free" is the agent's belief that the chosen action was unimpeded by factors not under the agent's control.