Do mains cables make a difference??

[Pharos]

Yes, electrons do oscillate around in a heat dependant random manner which is Brownian motion producing thermal noise, and this manifests as the noise audio wants rid of.

I wrongly didn't state that the velocity was an average, and refers to electrons being 'driven' by an applied voltage, which results in a velocity of only a few mm/sec.

Can't remember all of the noise types but shot noise, partition noise, and flicker effect come to mind. (college 45 years ago).

V (noise) = root (4kBTR) volts, where k = Boltsmans constant, B = bandwidth, T = absolute temperature, and R = resistance.