Power output of tube amps compared to solid states

Kirkus, Thanks! Your explanation of longer duration of headroom makes a lot more sense to my ignorant understanding of things than any of the other explanations offered so far.
I hate to use "my" current amplifier as a point of contention, but, my scope is somewhat limited. The manufacturer of my older cap coupled ss amplifier claims that it can double it's rated output for up to a couple of minutes at a time. Is that realistic? Is it due to it not being DC coupled design? Is it something all together different? What about ss amps like the Ayre that use chokes? I guess what I'm asking is whether tube amplifiers will always have this advantage over ss, or is it a matter of application?
It would appear to me that, while what you posted might very well be true, ss can usually offer more steady out-put power for the same dollar as most tube amplifiers. If so, wouldn't that negate some of the advantages you suggest for tube amplifier headroom duration?

Kirkus, "the particular set of energy-storage dynamics between a typical tube-amp power-supply and that of a typical solid-state amp are VERY different." Thank you for your insight! Finally, we now have something that tangibly advances the conversation.

My position throughout this thread has been that we are clearly measuring the wrong things (the most obvious being WPC), and that we need SOMETHING to bring us into the world of calculus, as opposed to arithmetic/algebra. Again, the complex relationship of loudspeaker/amplifier/music is not a static or steady state, but a dynamic phenomenon. Distortion, another steady state parameter, is most definitely not the answer.

What Kirkus has laid out on the duration of dynamic headroom pushes the discussion into the promised land of calculus. For that, praise, admiration, and congratulations are in order. Again, I thank you!

Do tubes have the same "advantage" in preamplifiers?

"Do tubes have the same "advantage" in preamplifiers?"

That's a good question! For many like me with tube-unfriendly speakers, the pre-amp (and source perhaps) are the practical places to introduce tubes.

I love my ARC sp16 tube pre-amp, but I do wonder if a good SS pre-amp could also deliver for similar cost or less once the speaker/amp optimization has been achieved.

I think they do. It would be really tricky to build a zero-feedback transistor preamp. With tubes you can do three stages of gain between the LOMC phono input and the line out, I doubt that the same can be said of transistors, at least, I've not seen any so far.

I have an additional comment about distortion that Joe mentioned- that of, shall we say, 'dynamic distortion'. Its my opinion that we need some sort of distortion test that uses a non-repeating waveform similar to what you see in real music. What Chaos Theory is saying about this is that sine waves represent a stable state in an amplifier circuit that might otherwise have chaotic response. BTW Norman Crowhurst pointed this out 50 years ago in his writings about negative feedback. Chaos Theory really seems to point to the idea that negative feedback is a destabilizing factor in amplifier circuit design, in fact, going so far as to call it non-linear.

This seems to fly in the face of traditional theory, where negative feedback occurs as something to increase linearity. But what we find by its application is that the energy of the distortion (nice calculus segue here BTW) is not changed at all- it is instead spread over the spectrum as a harmonic noise floor injected into the circuit's output. In addition, in-harmonic distortions are created due to inter-modulations at the feedback node.

The way the ear deals with this is interesting- our ears can penetrate natural noise floors like hiss or the wind blowing by about 20db, but can't do the same with this harmonic noise floor, which thus masks detail that exists below it. This is one reason why zero feedback circuits tend to be more spacious.