One of the most underrated component of any listening system is air. I know it sounds crazy but hear me out.
First of all, it's widely known that moving parts are extra important in the system and air is not some non-moving useless BS gear like a DAC or an amp, in fact (and this is very important) hearing is just our ears picking up the air's movements and vibrations. Imagine that, we don't even listen to the headphones or speakers, we actually just listen to the air's movement, this is why it plays such an important part in the HiFi experience. The connection between our ears and the air is just so direct and intimate.
As such, it absolutely baffles me how even some of the most seasoned audiophiles would simply overlook their dedicated listening room's air quality. Certain parameters of the air just change over time, no matter what. And I can tell you all from experience that it has a huge effect on the sound.
Back in the days when I was a newbie, I didn't understand why my headphones sounded so bad after airing out my room. It lacked a certain control overall but it was especially noticeable on the higher end of the spectrum. The highs always sounded unbearably harsh and really grainy right after the airing. Of course this effect would go away over time, the cans would start to sound more like I was remembering it, the control came back the highs smoothed out, the graininess went away and the top octave became more airy with more use generating a bigger soundstage, well until the next airing. It actually took me an embarrassingly long time to figure this pattern out even though looking back at it, it seems obvious. Using the same room of air for too long eventually caused everything to sound kind of cramped in and the soundstage became way too congested for my liking. The air also gets smellier and smellier over time. So don't overwork your room of air either.
Of course the air breaking in doesn't magically happen overnight and I believe it would never break in if there wasn't any vibration for the air to transmit. However, this would only happen to highly sound isolated environments and I don't live in a multimillion dollar recording studio. Under my circumstances, the air typically breaks in pretty much perfectly in just under a week. I found out I can speed up this process by various degrees using different methods. Running headphones for example could shave off about 2~3 days while using my floorstanding speakers always did the job in just one afternoon/evening. I've never tried to use anything specific like noises or signals for burning in my air, I have always used music for this. My neighbours probably prefer it that way too.
Burning in your air isn't the only thing you have to do the ensure your air is good quality. In my experience running a fan in the listening room (even when not listening to music) is generally a big no-no, this also applies to the fans in the computer (if you happen to use one in the same room you use for listening). It can undo the whole process of the burn in.
I also installed some random AC unit in my room in the early 2010's and if I wanted to use it, it would noticably tip my system's signature towards the cold side. I had the beyerdynamic T90 without a tube amp at the time so this definitely didn't help. I ended up returning the unit to the seller because that was obviously unacceptable to me but when I told them the reason they looked at me like a lunatic. With a little bit of persistence I managed to get my money back spent on the AC but not on the installation. After some research and digging I went with a mitsubishi AC system and I still use it to this day. While using it still makes the sound a little bit more bright it does so in an unitrusive way. It turns the sound more analytical and the sound becomes more detailed it does so without putting extra strain on my ears.
So the burn in of moving parts of the system is definitely real. Also a lot of audiophiles seem to overlook their crappy air quality for some reason.