Hi Caesar. I am too old and cranky on this topic to be asked about it.
So everyone else, please ignore.
Three points, one philosophical:
1. Equipment better meet their spec and subjective sound fidelity when you get it. If it doesn't after you pay thousands of dollars, I would move on. If such burn-in is required, it should be done by the manufacturer and not on my dime and time. I.e. Jack is right.
2. Individual components may change electrical characteristics with time. These changes are highly complex and unpredictable. Even more unpredictable is the fact that every electrical component already comes with wide variation (relative to these changes) when you source them. A 1% resistor is thought to be "precision resistor" and that is a heck of a lot of variation when you consider how many resistors are in your electronics, many of which are not spec'ed at 1%. Electrolytic caps are shipped with very large variations. Manufacturers try to hand match some components (e.g. output transistors) but there is not enough people in the world to hand match all the components in one amplifier!
Thankfully, circuits are designed to be highly invariant in these regards. And if there is variation, there is no telling if things get worse, instead of better with use.
3. Our hearing is highly elastic. One minute we hear minute detail because we are paying attention, another minute we are not. In my case my allergies go up and down causing severe changes to my high frequency detection. Such variations are huge and provable. Relying on such to determine atomic level changes in components is just crazy to me. If changes exist at component level, then you need to use invariant and much more sensitive tools to measure it (i.e. instrumentation). Using your ear would mean performing brain surgery on yourself.
Improper conclusions drawn on our faulty hearing impression explains why burn-in process is used. We think XYZ upgrade should make things sound better. We deploy it and it doesn't do that. We then wait and read into it said changes, validating two faulty promises.
Told you I was too old and cranky on this topic.