That's not entirely true, is it? When linear phase EQ exists I mean.
It is actually true, at least to the best of my knowledge, but I see how terminology like "linear process" and "linear phase" can cause confusion. I'll do my best to try and explain the difference in plain language without going too deep into the formalities of signal processing theory.
A linear, time-invariant (LTI) system or process is one that acts the same regardless of signal level or the point in time where you apply it. It doesn't remember what happened before and doesn't create new frequency components. It just applies a constant change to the input signal.
A simple example of such a process is a volume control (just changes signal level between input and output) or EQ (manipulates the signal frequency magnitude or phase responses, or both, in a constant way).
Linear phase EQ and minimum phase EQ are therefore both linear processes, the only difference between them being how they affect the phase of the signal. Minimum phase EQ will modify both the frequency magnitude response and the frequency phase responses together, and a linear phase EQ will modify just the frequency magnitude response and will not touch the frequency phase response.
Here's an example of minimum vs linear phase EQ in IK Multimedia ARC:
On the other hand, a non-linear process is something that doesn't satisfy the above conditions.
Typical examples of non-linear processes are distortion (it adds new frequency components - harmonics, which also change in level with input signal level) and dynamic processing such as compression (where output changes based on input level).
As such I don't know how the downstream EQ circuits on a bass / treble or loudness in a Yamaha amplifier works.
If a signal is passed through networks of inductor or capacitor to manipulate it, what happens to the "finished" signal after both Dirac and analogue EQ?
Adding EQ on top of EQ is basically just multiplication of the two EQ responses in the frequency domain (which is equivalent to convolution of impulse responses of both EQs, as
Fourier transform theory teaches us).
I.e., you could basically build one single EQ filter that is equivalent to what Dirac Live processing + Tone control processing does, if you know their individual responses.
Dirac writes this on their website:
"Dirac Live delivers phase alignment, speaker driver alignment, room resonance reduction, and e"
From my tests, Dirac Live "Phase alignment" comes mainly from use of minimum-phase filters (which also solve room resonances) and constant delays (to time align loudspeakers at different distances); and speaker driver alignment comes from use of all-pass filters (a type of non-causal EQ normally implemented as FIR) to counteract crossover filter phase wrap. These are all types of EQ filters.
The part that I suspect is not just EQ is Dirac Live ART - but as I said, I haven't really looked into how that works in any depth.
Hope this was interesting and (even better) useful!