How much does volume matter when breaking in amps and cables?

Oh, which means in geoffkait's case I have no explanation.

Absolutely none at all. Zarathu is right. There may be some speakers that loosen up in the bass after a few hours but that is about it. This myth got started by dealers telling their customer who were not sure that they liked a new piece of equipment, "you just have to let it break in." In a few weeks they get used to the sound and everyone is happy but in reality nothing changed. This break-in myth is the ultimate BS of all BS. The manufacturers do not want to say anything against it because the they do not want to alienate potential customers plus they can always use the break-in excuse. In reality it is not your equipment breaking in, it is your brain breaking in.

Ozzy, Purely anecdotal. cbrents, I worked in three dealers selling very high end stuff and for the most part we treated our customers like children. Which does not mean we didn't bend over backwards for them just that our explanations to smooth over issues was anything but scientific. So in part we were probably responsible for several popular myths. My favorite was telling new Acoustat owners that you had to keep them plugged in for two weeks to let the charges settle down on the diaphragm any time they were discharged. How fast do electrons travel?
geoffkait, my wife does all that. She gets me to cook for her that way. She has not managed to get me to vacuum yet.

Geoffkait you should not treat aberyclark with such distain for telling you the truth. Your ears are indeed having trouble adjusting to the environment.

Geoffkait, I would measure input and output impedances along with distortion values and rise time. But if there was no change the mythologists would just say the wrong stuff was measured. I would love to get a serum porcelain level on them. 

millercarbon there is a huge difference between mechanical devices and electronic devices. Undoubtedly, electronic equipment drifts slowly overtime as some component values shift with recurrent heat cycles although I have never seen objective evidence of this. There is no electronic device that I know of that changes its characteristics in the first several hours of usage. Imagine what that would do to computers! Certainly tubes need to warm up and stabilize. Maybe class A or highly biased AB amps sound a little different after they heat up although having had several class A amps I have never been able to hear this and again have not seen any objective evidence of this. People come up with a bunch of fuzzy theories why electronics and wires need to break in. All of them conjecture, mythology. I can say that all the full range ESLs I have dealt with do require a period of loosening up. Their diaphragms are tightened up with a heat gun after they are mounted and they do relax over time. This only effects the very low end. Perhaps some dynamic woofers may improve with break in as you can imagine their spiders and surround loosening up a bit with use. But again I have never seen any objective evidence of this. 
I own two 911s a 2006 Speed Yellow C4S and a 2014 Guards Red Turbo S. Porsche's break in recommendation has always been "keep it under 4000 rpm for the first 2000 miles." Absolute torture but there is no substitute. 

Mechanical devices like speakers and automobile engines may have a break in period as things loosen up a little. Many amps particularly tubes amps and preamps sound a little better after they warm up for a few minutes. But, breaking in of electronic devices and cables is total and compete MYTHOLOGY perpetrated by "experts" in the audio business and believed by gullible individuals that do not know how to evaluate their own hearing which can change with barometric pressure. While I am at it, there are good cables and bad cables. Good cables do not alter the signal, bad cables do. It is much easier to make a good cable than it is a bad cable. Putting a fancy chain mail jacket on it or adding a box full of nonsense does not a better cable make. It doesn't even justify the higher price. Next I am going to get my head cut off by people who have to figure out a way to justify the ridiculous amount of money they spent on BS.

I feel better now:)

jL35, people do not buy expensive gear that they do not like. They buy expensive gear that is flashy only to find out that they do not like it then are told "Gee, you just have to break it in." People like geoffkait are suckered into believing that is true. 
Aberyclark, try not to buy equipment you do not like which admittedly is not easy. I cower to think how much money I have wasted over the years. It is always buyer be ware unless you are geoffkait then everything you buy is just wonderful especially after it breaks in. The only item that breaks in is your brain. Of course certain people, who shall go unmentioned have a hard time finding theirs. OK moderator, is that polite enough?