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

Millrcarbon. Funny you mention engine break in 

I managed a plant for Delphi back in the day. The saying was “break it in how you are going to drive it”. If something fails pushing the car a bit hard in the first few miles, it’s not the rpm’s it’s a faulty component. 

It is all quite real. Everything, ime, requires some time to break in, or " settle ", and this is determined by listening, nothing more, nothing less. No measurements, just listening. It is easier to hear, if ( 1 ) you have a system that is highly resolving ( 2 ) a system familiar to you; ( 3) constant, and consistent, with minimal changes in the system; ( 4 ) with music you have heard over and over again; ( 5 ) the ability to listen, with excellent, and sometimes, experienced listening; ( 6 ) , and with, maybe, a trained ear, to hear this break in, warm up, settling in. 

I agree. Just like leaving an amp on 24/7 vs listening right after a cold start-up. You just know when you listen.

In are head" any decent set of ears! listening to a resolving system can hear new cables, resistors, circuit boards, transistors, breaking in'.

Some of the best designers have acknowledged the " breaking in process" and if you think its in our head you need to change hobbies cause your clearly wasting time and funds on this hobby.