This subject comes up in Episode 278 of the Lucretius Today podcast, but I know it has been mentioned here before so I will look for and link any previous threads I can find. (This may also be covered in discussions about the god.) The issue is the proposition, which the Epicureans (at least Lucretius) apparently endorsed: "All things which have a beginning must also have an end." Related questions are "Must all living things die?" and "Does anything exist eternally the same except atoms and void?"
It does not strike me as completely clear that Epicurus endorsed as a general rule of physics that "all things which come into being must also pass out of being," but closely related concepts seem to appear in Lucretius.
Here is how it comes up in "Tusculan Disputations" Part 1 section 32:
QuoteM. You take it right; that is the very thing: shall we give, therefore, any credit to Panætius, when he dissents from his master, Plato? whom he everywhere calls divine, the wisest, the holiest of men, the Homer of philosophers; and whom he opposes in nothing except this single opinion of the soul's immortality: for he maintains what nobody denies, that everything which has been generated will perish; and that even souls are generated, which he thinks appears from their resemblance to those of the men who begot them; for that likeness is as apparent in the turn of their minds as in their bodies. But he brings another reason; that there is nothing which is sensible of pain which is not also liable to disease; but whatever is liable to disease must be liable to death; the soul is sensible of pain, therefore it is liable to perish.
Here's a passage from Book One of Lucretius:
1-511 : Again since there is void in things begotten, solid matter must exist about this void, and no thing can be proved by true reason to conceal in its body and have within it void, unless you choose to allow that that which holds it in is solid. Again that can be nothing but a union of matter which can keep in the void of things. Matter therefore, which consists of a solid body, may be everlasting, though all things else are dissolved.
And from book five:
5-235: First of all, since the body of earth and moisture, and the light breath of the winds and burning heat, of which this sum of things is seen to be made up, are all created of a body that has birth and death, of such, too, must we think that the whole nature of the world is fashioned. For verily things whose parts and limbs we see to be of a body that has birth and of mortal shapes, themselves too we perceive always to have death and birth likewise. Wherefore, when we see the mighty members and parts of the world consumed away and brought to birth again, we may know that sky too likewise and earth had some time of first-beginning, and will suffer destruction.
I am not able to find an exact equivalent in Herodotus, though I may be overlooking it.
So the question comes down to: How close does Epicurus come to taking the position that "All things which have a beginning must have an end."
Is that some kind of natural law? Is it an Epicurean position?