What comes out of the turbo is cork screwing, swirling, and pulsing, with some pretty nasty shock waves.
Total silence requires a constant perfectly steady gas flow. That simply cannot be achieved without introducing at least some pipe volume and back pressure.
However, you can make the best of a bad situation with a bit of insight, and by being a bit clever about it.
Up near the turbo it needs a reasonably large pipe, especially the first couple of feet, and the sharp bend immediately after the turbo. Three inch is fine there.
Once it gets about half way down the car, the shock waves, bark and crackle, are still pretty strong, and the exhaust is still pulsing, but at least most of the gas is now headed in the same direction. Its here you can gradually taper the pipe down to 2.5 inches over a foot or two, just before it passes under the rear driveshaft without introducing much extra pressure drop.
Now if the main muffler behind the diff introduces a bit of slight back pressure, it can smooth out the exhaust pulsations, and it can be a 2.5 inch muffler.
The volume contained in the pipe up to the rear muffler acts like a big expansion chamber, and introducing a bit of back pressure after that, can reduce the low frequency pulsations, and the muffler itself, if its of the absorbtion type, will absorb much of the really objectionable high frequency energy.
That leaves you with two remaining problems.
The long section of pipe between the turbo and the rear muffler will have a specific length, and at one particular rpm, its going to resonate and drone.
That drone can be fixed by fitting a quarter wavelength J pipe before the rear muffler. Google "eliminate drone" and "J pipe" there is a great deal of information on the internet on that particular subject.
Last problem. The main muffler is a bit of a problem, in that a large bore open muffler will not have much pressure drop at idle and constant freeway speed, and it may still be more noisy than you want. If the main muffler has enough restriction to reduce the noise, its going to have too much pressure drop flat out.
So the trick is to add a special smaller muffler after the main muffler that has a spring loaded flap valve inside. This introduces a pretty constant 0.5 psi pressure drop, and acts like a blow off valve. At engine idle and steady road speed, it closes almost right down, and HUGELY reduces noise. When you are trying a bit harder with more throttle opening, it opens right up, but at that point the main muffler is starting to work properly. Many top end high power cars use this technique these days, so they are respectably quiet but still go pretty hard. The spring loaded flap type small 2.5 inch muffler to get is the Dynomax VT muffler.
These are supposed to flow 800 CFM wide open (363Hp) still with only about 0.75 psi pressure drop.
I have no connection to Dynomax, but I think this unique device is something we should all be aware of.
Its possible to have a respectably quiet exhaust that has about 1 to 2 psi total pressure drop absolutely flat out, and about 0.5psi the rest of the time.
The only manufacturer that I know of that publish full specifications for flow, HP, noise reduction and pressure drop are Donaldson mufflers.
These are robust industrial mufflers made in the USA for large trucks, tractors, and stationary applications.
I have been thinking about a style three, 2.5 inch M065140.
613 CFM (278Hp) 2" Hg drop (1 psi) and 14 dba attenuation under those conditions.
It won't do much just by itself, but assisted by a Dynomax VT, with which I am very familiar, should I expect do rather well as a combination.
le sigh