This discussion parallels the one on cables.
The cable industry frequently advises that cables be used for a number of hours of "burn in time". Metallurgists and scientists know that, at the voltages and currents used in the audio industry, the notion of changes occurring in the physical or electrical properties of copper wire is utter bunk.
The real issue is psychoacoustic, where the brain requires time to hear what it wants to hear. I think the same thing applies to source material, playback devices, amplifiers, and loudspeakers.
So how is this for an idea: We accept the objective measurement of devices. We audition devices meeting certain performance thresholds (20-20 kHz +/- 0.5 dB, THD+N under -116 dB, etc.). Provided an audition falls within a broadly acceptable range of performance, we then allow our ears to burn-in.
Musicians would call this training one's ear to recognize certain tones, pitches, rhythms. We might call it training ourselves to be objectively better consumers.
I really hope some light will be shed within a reasonable period over cables, in a scientific way.
Cable manufacturers claim it's not the metal that needs the burn-in, but dielectric.
Their general explanation on how dielectric (outside of burn-in time issue) affects the signal is charge-discharge cycle: dielectric charges from the signal from the conductor, then discharges back to the conductor, but with some time delay. Some describe it as a time smear. I imagine it as an echo from the signal.
So to determine whether this is true or not, I'd say we need a specifically designed measurement. Discharge from the dielectric won't supposedly generate harmonic or non-harmonic distortion because it follows the original frequency. Instead, distortion supposedly happens in the time domain only - time delayed artifacts instead of changed artifacts.
So I guess cable measurement designed to prove or disprove whether something like this happens should use something like a signal impulse of a very short duration and then screen whether it generates additional waveform (of a same frequency) in time domain, trailing the original signal impulse.
I point out, these are only my own thoughts/speculations on how the truth about this should be experimentally researched, based on what sounds logical to me.