Again, if all motion is always one long chain, and new motion arises out of the old in order invariable, and if the first-beginnings do not make by swerving a beginning of motion such as to break the decrees of fate, that cause may not follow cause from infinity, whence comes this freedom (libera) in living creatures all over the earth, whence I say is this will (voluntas) wrested from the fates by which we proceed whither pleasure leads each, swerving also our motions not at fixed times and fixed places, but just where our mind has taken us? For undoubtedly it is his own will in each that begins these things, and from the will movements go rippling through the limbs.
The essay quotes numerous modern commentators regarding the fact that both Lucretius and his philosophical mentor Epicurus refuted Democritus' idea that the doctrine of atomism implied absolute determinism. Particularly puzzling to modern minds is the idea that the ultimate source of "voluntas," Lucretius' word for free will, is to be located in the movements of infinitesimal atoms. Both men, in trying to explain what physical forces caused atoms to combine with one another, spoke of a "swerve" (Latin clinamen) that had to take place for such combinatory action.
I'm not enough of a classicist to judge the complexities of archaic Greco-Roman culture; I can only say that of the comments cited in the Wikipedia essay, those of Don Paul Fowler seem most accurate in representing the way philosophers of this period framed their conceptual conundrums.
Lucretius is arguing from the existence of voluntas to the existence of the clinamen; nothing comes to be out of nothing, therefore voluntas must have a cause at the atomic level, viz. the clinamen. The most natural interpretation of this is that every act of voluntasis caused by a swerve in the atoms of the animal's mind....There is a close causal, physical relationship between the macroscopic and the atomic.
I don't believe any reputable philosopher today would subscribe to the idea that non-sentient atoms can display "will" of any kind. However, the Epicurean swerve may still be a useful metaphor for the nature of human agency, and it does resemble one of the models constructed by theoretical biologist Stuart A. Kauffman. I examined Kauffman's concept of "quantum coherence" in my essay LET FREEDOM RIDE PT. 1:
There is a possible objection to Kauffman's philosophy. In REINVENTING THE SACRED he does not manage to show in what way his principal of "quantum coherence"-- proposed as a principle that may have contributed to the formation of the "open thermodynamic systems" of living organisms -- makes the subject's will an "uncaused mental cause." In the view of most reductivists, if quantum-energy factors did influence the formation of life on our planet, those factors would just be another set of contingent influences, as much as the sun's radiation or the presence of oxygen. Kauffman repeatedly explains his title by saying that humans do not need supernatural forces to explain life any more, but that humans should regard their own "agency" as sacred.
Kauffman's insistence on validating the "sacred" human world of culture strongly resembles the attitude of the Epicureans, though he doesn't cite any of them in REINVENTING THE SACRED. Persons of a reductive viewpoint will of course dismiss "quantum coherence" as quickly as they will dismiss the "Epicurean swerve," but as I've stated many times on this blog, I don't believe philosophy should be determined by the data of experimental science. Metaphors for the way the human mind works-- or even discrete parts of the mind, such as "the heart" or "the imagination"-- will always be not only necessary, but entirely preferable to reams of dubious data.
In closing I'll note that because Lucretius shares the Epicurean belief that "nothing can come from nothing," he takes a rather "atomistic" approach to the human imagination as well. He asserts that although there is no hell, humans have extrapolated their experiences of earthly pain into the torments of Avernus. Similarly, though centaurs and "the spectres of people who are dead" have never existed, these are imaginary composites formed from humans' tendencies to combine the forms of nature, be it hybridizing humans and horses to produce centaurs, or simply imagining formerly-living people taking on a quasi-physical existence in the form of ghosts. I gave some thought to the possibility that I might view Lucretius as early advocate of that form of sublimity I've named the "combinatory-sublime." But though Lucretius may be writing about roughly the same creative process that Tolkien described as a "refracted light" that is "endlessly combined in many shapes that move from mind to mind," Lucretius doesn't share Tolkien's fascination with the process. Lucretius is a poet in the tradition described by Chesterton: "one who is in love with the finite." ON NATURE is full of colorful descriptions of erupting volcanos and burgeoning fields of grain, but all of these images are for Lucretius mere evidence of the world's conformity to physical law. For Burke and Kant, a volcano might be something that evoked in human beings the feeling of the sublime-- but I suspect such a volcanic emotion would have run contrary to the equanimity endorsed by Lucretius and his fellow Epicureans.