The process that happens in your brain is quite different than the way electronic components burn-in.... and how it occurs, and how quickly, depends on a lot of different factors.
One classic, and somewhat disconcerting, way to demonstrate this is very simple.
Fill one container with cold water... and fill another with hot water...
Put one hand in each container at the same time for a minute or two.
Now put BOTH hands in the SAME bowl of room-temperature water.
Your brain will have fun trying to figure out how one hand can be in "warm" water, while the other is in "cool" water, but you can see both hands - in the same bowl.
For most people, this "calibration effect" only takes a minute or two.... think about the amount of time it takes for your bath water to no longer seem hot.
Photographers and other artists are very familiar with this experience as it concerns color.
Sunlight, skylight, fluorescent lamps, and incandescent lamps, are all very different colors.
Yet your brain does such an excellent and seamless job of correcting what you think you see that a white piece of paper looks "white" in all of them.
(But turn off the auto-white-balance on your camera and take a picture under each.... you'll see that the paper
REALLY looks yellow under sunlight, blue under the sky, and probably greenish under the fluorescent lights.)
There are limits to these effects... but those limits are a lot further apart than you probably think.
Because the act of hearing is itself very complex, the effect of "normalization" is also more complex, and can occur along many different axes.
It's also strongly influenced by your perception - and your concentration and focus.
With audio, most people notice this effect most strongly with speakers, which tend to have the most variation.
Your current speakers sound "normal".
Then you buy new ones.
For the first day or two your new speakers sound "bright".
But, by the end of the first week, they probably sound "normal".
And, now, when you pull out your old speakers, THEY sound "dull" and "laid back".
Guess what?
The speakers haven't changed.... your brain has simply reset it's frame of reference.
This effect can be really insidious if you design and build speakers...
You're busily trying to tweak your new project to sound the way you think it should.... while your brain is busily tweaking itself to consider what your project sounds like today as "normal".
(So you should make a point of having a reference, and going back and forth between your project and the reference - to avoid having YOUR calibration "drift over time".)
(To make matters worse, new speakers really DO mechanically break in over the first 100 hours or so of play... so there are some real changes mixed in with the illusory ones.)
The process is also strongly influenced by our personal biases and expectations.
(After all, when you hear a difference between your old DAC, and that expensive new one everyone is raving about, you EXPECT the new one to be better instead of worse, right?)
So, if you want a really fair comparison, buy that new DAC, then let it sit in the next room "burning in" and "reaching equilibrium" for a week or two.
At the same time, continue to listen to your old DAC.
(Or, even better, don't listen to either one for a week or two.)
NOW you can compare both, with both "fully burned in" and "fully warmed up", and no calibration problems.
(Or, even better yet, go and listen to LIVE BANDS for a week.... then come back and see how each of those DACs compares to the REAL reference.)
Incidentally, if you REALLY want to see how or if a component changes when "burned in", it's really easy. Get TWO samples of the same DAC, let one "burn in" for two weeks playing music; leave the other one in the box; NOW, after that two weeks, turn them both on and compare them. (This would only really be practical if you have a buddy who lives nearby who is considering buying the same one... but it should be practical - and useful - for a reviewer to do it. It would be even cooler to try it after a half hour, when the new one is fully "warmed up", and compare that to one that's "been burning in for several weeks".)
IME, it's not so straightfoward that the differences you hear after a prolonged duration especially. Our memory are not that good to compare subtle differences from recall especially. That is not all, we are not like a DAC or a circuit, we have conditions(our conditions change), and our auditory system is tied to the brain that has bias from the overal sensory and predispositions. We have emotions, feels, etc.. What we hear at one moment can change, and out auditory conditions change. Our brain/ears has a way of adjusting. Unless we do a precisely controlled experiement, these opinions have too many variables that should be considered to be certain especially considering human subjectism is involved. There's more variables.
@KeithEmo
Thanks for laying all of this out. I have not doubted that people are hearing what they report. We have some very expert listeners here. I have, however, had exactly the same impression about why as you just posted. I am sure you will be told you are all wet, but then we both will be. I am also of the impression that we don''t hear a whole piece of music consistently each time we play it. The brain is an amazing processor. Much like a DAC it reconstructs a coherent sound from soundbites. Each time you listen your brain samples different bytes (if you will). By the time a week's burn-in has completed, you've done a pretty job on sampling most of what a piece of kit sounds like. That helps make it sound like it's changing with time.
Now here's a question for you. How do you explain the results for those who get a new DAC, turn it on, listen to it once, feed it music for a week and then listen to again and declare it has undergone an amazing transformation? It would seem like they have not had a full brain burn in yet nonetheless they report changes with time.