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

I don't think the amount of volume is going to make any significant amount of difference.  I have burned in many cables, including speaker, at just low to moderate volumes.  Consider this.  Digital type cables (including spdif and hdmi) will typically only push 0.5 to 0.6 volts on the data conductors.  However, analog audio can be up to 1.4 to 2 volts.  In either case, both cables can be burned in with similar timelines.  Speaker cables will see significantly higher amounts of voltage (such as 5-50 volts or more, depending).  I think it's more important to send an amount of charge/discharge activity down the wire to help break it in.

I enjoy few things more than listening to a component as it burns in. The changes are just fascinating, especially the first few minutes to hours. Speakers, amps, cables, even fuses. Just one of the most amazing things, and I listen closely every time. In 20+ years I have heard no evidence volume matters at all. 

Geoffkait -  "Use blankets or jeans over speakers to mute the sound"

Good grief are you fat or what?

Buy a  good breakin cd that uses a lot of sweep signals like the purist audio, or anther we’ll know CDs just play. On repeat or burn to your hard drive I have done this many times cut runin time 
by at least a 1/3 rd also shut off for a 1/2  at least 1-2 x a day 
for it discharges the. Capacitors  then you reenergige them 
it help with cap breakin . Being around audio almost 40 years 
have got a lot of good tips through electronic tech friends.