OK. I think I see where our signals are getting crossed. I look at your diagram and think, The green signal
g is not what you get when you try to output the red signal
r but the output stage clips it at the supply voltage (my
V). Rather, the green signal
g is what you get when you take the red signal
r, amplify it by
A = Infinity, and
then try to output that new signal
rA, which the output stage then clips.
For all A > 1, |rA| > |r|. Therefore, I have no problem agreeing that a clipped rA carries more energy than the original r. (In fact, this is just saying that bigger signals carry more energy, regardless of clipping.)
To me, your original statement read as though it made the following claim: If your amplifier tries to output a signal r but clips off the peaks, what you get out is a signal that carries more energy than r. (This is the claim I found hard to believe.)
But what you really meant (I think) was that, if you take a sine wave as input and, as a human controlling the volume knob, keep turning up the volume until the sine wave's maximum amplitude so far exceeds what the amplifier can reproduce that it comes out looking like a square wave, then that square wave carries more energy than the original, un-volume-adjusted sine wave. Is that what you meant?
If that's what you meant, I have no problem believing your claim. It's just that I wouldn't call turning up the volume knob to be part of the "clipping" process, but rather amplifying. When you turn up the volume knob, what you get out is always a "bigger" signal, even if it's clipped.
