Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty
What is your claim, that disorder, randomness and uncertainty DO NOT build up with time? :)
> And I agree that tests make refactoring easier.
They don't make it easier. They make it POSSIBLE.
> And so, what specific quality guarantees do good tests make?
Good tests cover all critical sections of functional specification (what is deemed critical depends on project). If you have functional rules x, y and z somewhere there, there need to be bunch of tests for x, y and z somewhere, ideally fuzzy, fast and without blank database.
This is all very much basic IT stuff for long time, particularly nowadays when software needs to run not only in your basement but on every conservable device and number of different contexts!
No offense, but you seem new in this business, and your aggression doesn't help at all.