I learned about the relationship between efficiency and thermal compression from a recording engineer who posts over at the Audio Asylum under the moniker "RBP".
The following is taken from RBP's post:
"Over the last 25 years, I have studied a factor that is not getting the attention it deserves. I have written several papers on this. Call it Linear effeciency.
"Take two designs, Low eff. and High eff. Even though "High eff. is still considerably less than even 10%, these results will prove why higher effeciency Loudspeakers are closer to the truth that Low effeciency in terms of dynamics. High effeciency has it's price. Usually more deviation in the frequency response curve, and large size, plus higher low frequency cutoff per cu ft.
"Here is a reprint of one of over 200 effeciency test I have performed over the years. Note that doubling the power does not necessary mean a rise in 3dB!
"From the Archives:
86dB speaker. DCM Time Window.
"1W.... 85.7 (2.4dB)
2W.... 88.1 (2.3dB)
4W.... 90.4 (2.2dB)
8W.... 92.6 (2.2dB)
16W... 94.8 (2.2dB)
32W... 97.0 (2.1dB)
64W... 99.1 (1.8dB) Severe compression here.
512W..Voice coil failure.
128W...126.6dB (2.4dB) Compression begins....
256W...129.0dB No need to go further risk speaker damage.
"White noise burst for 500mS (1/2 second)
"Clearly the difference between 1 and 128 watts on the Klipsch is 20dB. [actually RBP made an arithmetic error - the difference is 23.3 dB].
"The low effeciency speaker ..only 15.2dB"
This is very interesting. I asked RBP about the greater-than-3dB "expansion" figure for the Klipschorns. From his reply:
"I thought it was meter overshoot at first but my measurement system is deadly accurate....I get the same thing for 50mS as I do 500mS or even 5 sec. It suggests that there is a point (it is around 96dB...96.2 to be more precise) where you get an honest 3dB with power increase of double."
I haven't independently verified RBP's findings, but I think he's barking up the right tree. His measurements explain things I've been hearing in a good high-efficiency systems, but I still haven't found a high-efficiency system that doesn't have some little shortcoming that bugs me.
For example, using the numbers given by RBP, suppose we have a hybrid system with 86 dB woofers and 104 dB horns (padded down, of course). When the music signal says "give me a 20 dB peak", the horns would give you 23 dB while the woofers would only give you 15 dB. So, the speaker would sound bright and thin on peaks. In addition, it would have to be voiced to sound right at a particular sound pressure level - any softer and it's too dull; louder and it's too bright.
Note that with electrostats, different compression mechanisms come into play - there is no thermal compression because there is no voice coil to heat up. Compression in electrostats seems to be related to transformer saturation, among other things, as I've heard low-efficiency electrostats that compress audibly less than higher efficiency ones.