Quote from Could you please elaborate on how the swerve is a precondition for the existence of free will?
In both Democritus' and Epicurus' universe, particles and void are all there is. The distribution and movements of particles determine our reality including our thoughts about it.
In the Democritean universe, the particles behave like hard bodies in classical mechanics. The present and future distribution and movements are determined by the distribution and movements in the distant past. Therefore, the history of the Democritean universe including our thoughts are predetermined. We may still enjoy our pleasures but do so as concerned voyeurs (like sophisticated jumping Jacks who have feelings and are integrated in a moving clockwork), not as agents who invent and choose among options for their actions. Therefore, there is no free will in Democritus' universe.
In Epicurus' universe, a particle may deviate a bit from its mechanistically determined path. Therefore, the universe including our thoughts is no more completely predetermined by the past. Under this condition, free will may be possible.
In which species free will exists and how it arises is still a subject of ongoing research. The conclusions still appear to be speculative.
For the background, there are a number of difficulties with Epicurus' physics:
It is partially refuted, completely lacks the powerful mathematical modeling with which we are familiar and is rudimentary in comparison with what we learned with Galilei, Newton and many other physicists.
I see a strong enough analogy between Democritean physics and classical mechanics that I use classical mechanics for the Democritean universe. Others may see this as too farfetched.
As Epicurus' ethics are based on Epicurean physics, others may reject the whole philosophy because parts of the physics are refuted. I take the refuted parts as similar to refuted or abandoned scientific theories. These theories were stepping stones for the progress to recent science and do not refute the scientific method. Similarly, the refutation of parts of Epicurean physics does not refute the whole philosophy.
To formulate an Epicurean answer, I combine not refuted parts of Epicurean physics with modern science. Others may reject my approach as arbitrary, choose a different approach and come to different conclusions.
Sedley's article referenced by Cassius above is probably a good read for the topic.
although I do not fully agree with it. According to comments on a Facebook forum, it is quite tough for non-scientists though.